Mercedes technical director James Allison says the team were left "embarrassed" by Lewis Hamilton's disqualification from the United States Grand Prix for a breach of technical regulations.
Hamilton and Ferrari's Charles Leclerc were excluded from second and sixth places respectively four hours after the end of Sunday's dramatic race after wear levels on the planks underneath their cars were found to have exceeded limits set out in F1's regulations.
The seven-time world champion's disqualification means that instead of closing to within 19 points of Red Bull's Sergio Perez for second in the drivers' standings, his deficit grew to 39 points with just four rounds of the season remaining.
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Speaking in Mercedes' post-race debrief, Allison said: "Of course the disqualification is a significant blow. It's a miserable feeling. It hurts and, everybody here feels it.
"Everybody is upset, embarrassed to a degree as well because we absolutely don't like being on the wrong side of the rules, and just lamenting the lost points."
After Mercedes brought a final significant upgrade of the season to the W14, Hamilton produced a hugely impressive weekend which saw him narrowly lose out to the other Red Bull of world champion Max Verstappen for victory.
Allison said that the progress made in terms of performance will help the team get over the disappointment of the disqualification.
He added: "Give it a day or two and that will start to wane and be replaced by the much happier feeling, which is we moved our car forward this weekend and that it's hard to do that.
"But we did it and we did it by a decent amount. And with four races left in the championship, four races where I am pretty sure we will stay on the right side of the skid block rules.
"The initial feeling of hurt, and disappointment and frustration of ourselves will pass to be replaced by the sunny optimism of knowing that the car looked bright on this upgrade package and we've got four more races to show what we can do with it."
'We made a mistake'
Allison also gave a detailed explanation of how Mercedes fell foul of the regulations, accepting that the team had made "a mistake" by failing to leave enough margin.
"The disqualification had everything to do with the setup and the bumpiness of the track, amplified by the fact that it was a Sprint weekend," he said.
"At a sprint weekend, you are under much more pressure, you have just a solitary hour at the very front of the weekend.
"After that one hour basically, you have cast your die, you have chosen your setup and you have then got to run the rest of the weekend with the bets you placed in that one hour of running. That means much, much less time to assess things than normal and much less time to make corrective action ahead of the remaining sessions later in the weekend.
"Austin is a track which has a very bumpy surface and therefore you are a bit more vulnerable to bumping the car on the ground. We just simply didn't take enough margin at the end of Free Practice 1.
"When we had done our setup we checked the plank and everything, all looked fine, really untouched after the FP1 running. But the results of the race speak for themselves. We were illegal at the end of the race so clearly, we should have had our car set a little bit higher up to give ourselves a little bit more margin.
"It's of course a mistake, it's an understandable sort of mistake in a sprint weekend where it's so much harder to get that stuff right, especially on a bumpy track. But a lesson for us in the future to make sure that we take more margin, especially at a track like that with all its bumps."
How Hamilton strategy gamble fell 'crushingly' short
The pain of disqualification could have been even more extreme for Mercedes had Hamilton ended a near two-year wait for his 104th F1 victory, which very nearly happened.
The Brit was closing on Verstappen rapidly in the final laps of the race but could have already been in front of the Red Bull if it weren't for a poor strategic call from Mercedes.
With Hamilton running second behind Lando Norris and in front of Verstappen, Mercedes chose not to react to Red Bull bringing the Dutchman in, opting to attempt to implement a one-stop strategy as opposed to the two-stopper the other contenders had committed to.
Hamilton's tyres fell away a couple of laps later, by which point he had lost track position to Verstappen and then had to fall back onto a less optimum version of the two-stop strategy.
Their respective pace for the remainder of the race, with both comfortably faster than Norris' McLaren, suggested that Hamilton would have had an excellent chance of victory had Mercedes reacted immediately to Red Bull's stops.
Allison explained that Verstappen's dominant performance in Saturday's Sprint had left Mercedes convinced that Hamilton would not have the pace to beat him on the same strategy.
"We should have pitted Lewis, we should have kept ahead and we would have given ourselves a better chance of the win had we done so," Allison said. "But it's good to understand where we were coming from, and also understand a bit more of the strategists' dilemma.
"We knew that we had been pretty pacy during the Sprint race the day before, but we also knew that Max just had the edge on us.
"Austin being the sort of track where generally speaking the track sort of tends to deal out the cars in pace order by the time the chequered flag falls at the end of Sunday, so we didn't actually think we were in exactly the same race as Max."
Given that belief, Mercedes believed their best chance of victory was by running an alternative strategy, and they thought a one-stop was possible as Hamilton maintained strong pace late into his first stint.
"We left Lewis out there and waited to see what would happen, hoping that the flat lap time progression would continue," Allison said. "A lap went by and we'd effectively been undercut and then we were just crossing our fingers to see whether the pace evolved as we hoped.
"But, rather crushingly, within a very short period of time after we had lost the ability to protect against Max, after a long period of flat lap times with Lewis, his lap times turned south on us, and we experienced the same degradation as everybody else, turning us into a two-stop car along with everybody else, but having surrendered the position to Max in the first instance as a result of that false optimism that we could make this one-stop work.
"Whereas we definitely would have been better to cover him off because actually the raw pace of the car was good enough to compete on equal terms with him and if we had just done a two-stopper against his two-stopper, it could have been a different race."
When to watch the Mexico City GP live only on Sky Sports F1
Thursday 26 October
9pm: Drivers' Press Conference
Friday 27 October
7pm: Mexico City GP Practice One
8:45pm: The F1 Show
10:45pm: Mexico City GP Practice Two (also on Sky Sports Main Event)
Saturday 28 October
6.15pm: Mexico City GP Practice Three
9pm: Mexico City GP Qualifying build-up (also on Sky Sports Main Event)
10pm: Mexico City GP Qualifying (also on Sky Sports Main Event)
Sunday 29 October
6.30pm: Grand Prix Sunday Mexico City GP build-up (also on Sky Sports Main Event)
8pm: The MEXICO CITY GRAND PRIX (also on Sky Sports Main Event)
10pm: Chequered Flag: Mexico City GP
F1 heads straight to Mexico for the middle leg of the Americas triple header. Watch the whole Mexico City Grand Prix weekend live on Sky Sports F1 from Friday, with Sunday's race at 8pm. Stream F1 on Sky Sports with NOW