Blackburn pressed for the winner to help pull clear of the bottom three, but instead Carroll rose to head home in added time to put Liverpool within a point of seventh-placed Merseyside rivals Everton ahead of this weekend's FA Cup semifinal clash.
And it rescued a point for Liverpool who are now second in the group, behind Atletico on goal difference.
McLeish has guided his side to an impressive first half of the season and they are currently eighth in the Premier League table, just one point behind Liverpool.
The damaging defeat left Chelsea four points adrift of league leaders Liverpool and only a point ahead of United, who have two games in hand over their title rivals.
The victory leaves City level on points with fifth-placed Liverpool and only one point behind Spurs with two games in hand over both rivals, although boss Roberto Mancini will be grateful for three points following one of their less convincing performances of the season.
With this in mind, Dr Lewis said there was no point in visiting Liverpool.
Bafetimbi Gomis lobbed in the fourth after heading the ball past Debrecen goalkeeper Vukasin Poleksic early in the second half, as Lyon established a three-point lead over Liverpool and Fiorentina at the top of the group.
United need one point to move clear of Liverpool with 19 title triumphs having beaten Chelsea 2-1 on Sunday.
What's most interesting and most critical for Liverpool's future at this point is how the club reacts going forward.
Mill Financial had reportedly emerged at one point with a bid of its own to purchase Liverpool FC, but was unsuccessful.
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It was the high-point of a 25-minute opening period in which Liverpool dominated possession but created few real goalscoring chances.
Third-placed Arsenal, who have a game in hand over Liverpool, return to Merseyside in a fortnight, and are just a point ahead of Rafael Benitez's side, who drew 0-0 with Aston Villa on Sunday.
At some point manchester united will have to realize what it is like to be liverpool.
Gerrard assumed a growing influence on proceedings but Liverpool lacked the finishing touch that Torres so often provides and were forced to settle for a point.
It's been on my mind to point out that although there may be a rational argument for placing the holding companies of Liverpool Football Club into administration, that may be technically impossible as of this moment.
Liverpool went behind to a deflected strike from former striker Craig Bellamy on Sunday before Dirk Kuyt rescued a point with a late strike.
Hugo Rodallega's 35th-minute winner came from a mistake by Dirk Kuyt, a point that was picked up on by Benitez, who has frequently promised during the season that Liverpool will qualify for the Champions League.
Liverpool are breathing down the neck of Tottenham who are currently in the fourth and final Champions League spot one point ahead and with one game in hand.
Liverpool had seen their title hopes ended after Manchester United beat them to the Premier League crown after getting the point they needed with a draw against Arsenal on Saturday.
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