Jurgen Klopp described Alisson's sensational last-gasp winner and emotional celebration as "really touching", after the goalkeeper incredibly kept Liverpool in the race for a top-four finish with his 95th-minute header at the Hawthorns.
With the game at 1-1 and Liverpool needing three points to keep their Champions League hopes in their own hands, the Brazilian charged forward and brilliantly headed in Trent Alexander-Arnold's 95th-minute corner.
Alisson, whose father tragically died earlier this year, was clearly overwhelmed amid the celebrations afterwards and Klopp, who has suffered his own bereavement this season, told Sky Sports he could feel what the goalkeeper was going through.
"We are really close so I know exactly what it means to him and what he thought in that moment," said the Liverpool boss.
"It's outstanding. It's really touching. It's only football but it means the world to us."
Reflecting on the moment Alisson became the first Liverpool goalkeeper ever to score in a professional game, Klopp said: "Unbelievable. I've never seen something like that. Insane technique!
"Nowadays you can't be sure, really. 'Is something wrong? It cannot be?' So I turned around to ask, 'Am I right, did he score?' And you saw the faces of the boys. It means a lot to us, obviously.
"We are still in the race. But Wednesday [when Liverpool go to Burnley] will be the same fight.
"I have to say 'chapeau' [take my hat off], West Brom fought with all they had, proper professionalism, and made it really difficult for us but we did it."
Up until Alisson's intervention, it had appeared Liverpool would miss the chance to put serious pressure on Leicester City and Chelsea, the two teams directly above them in the Premier League table.
Mohamed Salah had come up with a superb equaliser after Hal Robson-Kanu's opener, but, despite a series of shots at the West Brom goal, Liverpool were struggling to find a way through.
However, Klopp praised the attitude of his players and for sticking with their planned approach right until the end of the game. Liverpool's final two games are against Burnley at Turf Moor on Wednesday and Crystal Palace at Anfield on Sunday.
"The game is our season in a nutshell," he said. "We do a lot of good stuff, get pretty much hammered for the first mistake, and then have to work like crazy.
"I liked it. Nobody got over the top. It was 1-1, the minutes were going down, down, down but we had the best chances in the last five or six minutes. We had a shot from Thiago, from Gini [Wijnaldum], but we kept playing football. It's really difficult against this side, how they defend, how they set up, but in the end we needed Ali to solve it.
"Now let's keep going. Have a look at who can go again and make sure we're ready for Burnley. Our last part of the season looks quite exciting."
- West Brom 1-2 Liverpool - Match report and highlights
- Match stats | How the teams lined up
- Premier League table
- Get Sky Sports | Get a Sky Sports Pass
Allardyce: Officials cost us all three points
On the other side of Alisson's goal was Sam Allardyce and West Brom, who, despite already being relegated from the Premier League, battled impressively.
Boss Allardyce told Sky Sports he was unhappy with referee Mike Dean and the VAR officials for two calls which he felt turned the contest.
The first involved Dean awarding Liverpool a free-kick when he impeded Fabinho in midfield, while the second was an offside call against Matt Phillips when Kyle Bartley stroked in from a corner.
"It's hard to take after what you've done. We didn't want a result snatched away from us, not by Liverpool but by the decisions made today, and unfortunately two decisions are causing us a problem in terms of both Liverpool goals.
"The referee should give a drop ball, not a free-kick, for the first goal. That's a complete blunder as far as the rules go. Then the goal we scored that VAR is supposedly there to let a player who is onside score a goal, and don't give us none of the rubbish about 'he's in the goalkeepers eyeline' because he's about two and a half metres off him. That's just an outrageous ridiculous decision when you've got VAR.
"I said before the game we needed a bit of luck, we needed a great performance, and we didn't need the officials or VAR to go against us and they've gone against us on two occasions, and it's the main reason why we've lost this game today."