Jamie Carragher told Monday Night Football he didn't object to Jose Mourinho's tactics at Liverpool - but his approach against top-six sides could cost Manchester United the title.
United faced one of last season's top six for the first time on Saturday, but the result was an uneventful 0-0 draw and they had just one shot on target in the entire match.
Mourinho was described as an "enemy of football" in the newspapers on Sunday morning, but Carragher refused to criticise the Manchester United boss.
However, he says some harsh words may be due if United continue to play like that in big matches.
Carragher said: "First of all I should say I had no problem whatsoever with what Jose Mourinho did. He's always done it and I expected it before the game.
"Jurgen Klopp said afterwards that Liverpool could never play like that; well maybe his Liverpool could never play like that, but my Liverpool did and we did it plenty of times and got results on the back of it.
"I think the criticism will be saved until the end of the season if results in big away games don't improve and it costs Manchester United the title."
Mourinho has not won any of the last 10 matches his sides have faced away at Arsenal, Chelsea, Liverpool, Manchester City and Tottenham - and his team has not even scored in the last nine of those.
And Carragher, who was joined in the MNF studio by five-time Premier League champion Peter Schmeichel, feels those damning statistics prove that his approach in big games is not working.
He added: "Jose Mourinho has always been lauded - and rightly so - as the man for the big occasion, the man in a big game, a 'Mourinho masterclass' winning these games.
"His way, of late, is not working.
"I go back to when Peter Schmeichel was winning titles with Manchester United and they possibly had six big games - Liverpool home and away, Arsenal home and away and someone else challenging, whether it was Chelsea or Newcastle.
"That's 18 points. With the top six now that's 30 points. That's a big part of the season. You've got 10 games home and away.
"If that doesn't improve they won't win the league and that's when the criticism will come.
I think the criticism will be saved until the end of the season if results in big away games don't improve and it costs Manchester United the title.
"I won't criticise him for the way he played at Anfield because you can still win a game playing like that - but if those results continue I think it will be very difficult to win the title."
United now trail Manchester City by two points in the title race - and Carragher feels the results of the big head-to-head matches could prove decisive.
He said: "Manchester City have already got six points out of six in the head-to-heads with Liverpool and Chelsea.
"Manchester United have had one game and one point against Liverpool and it's a good result for Manchester United, not a bad result.
"But somewhere along the line he's got to pick up these points. If he doesn't, and City continue in the head-to-heads, that's where the criticism will come that he's been too negative."