On a poignant day for the club, marking 25 years since the Hillsborough tragedy, Brendan Rodgers' men raced into the lead with goals from Raheem Sterling and Martin Skrtel, but City clawed their way back after the interval thanks to David Silva and a Glen Johnson own goal.
However, Phillippe Coutinho's strike 12 minutes from time proved decisive as Liverpool moved five points clear at the top of the table ahead of Chelsea's match with Swansea.
Gerrard is aware of the importance of the win, but warned the title is not within their grasp yet and feels next Sunday's fixture at Norwich is now key to their hopes.
"That win means so much," he told Sky Sports 1. "They got back into the game but I think we showed today that we want to go to the wire. We want to go all the way.
"That's the longest 90 minutes I've probably ever played in. It felt like the clock was going backwards in some parts of that game.
"But that is such a big result for us. We've got four cup finals left. People said that was the biggest one (match) but I disagree - I think the biggest one now is Norwich.
"Nothing is ours yet. The important thing now is not to get carried away with that result. We need to stay calm and prepare for Norwich. The scenes are great today and the fans are very happy, but we have a day off tomorrow and then we go for Norwich."
Rodgers feels his team deserve all the plaudits for the spirit they showed in claiming maximum points having thrown away a two-goal lead.
He said: "I thought we were incredible today. We showed so much quality. To come back showed the character in this group - it's three very valuable points for us.
"We were well on top in the first half but they've got top players and top players respond. They very quickly got themselves back into the game, but we changed the shape again and the goal came.
"It was a wonderful atmosphere, pitch-side it was incredible, so between us all - players, supporters and staff - it was a great victory for us."
However, Rodgers side-stepped the question about whether Liverpool were now favourites to land the title.
"I said at the beginning of the game it was a significant game, and it may end up being a significant one," he said. "But we've got Norwich next week - they played well yesterday.
"We'll enjoy the win, recover well and concentrate on the next opponent."
Pellegrini was left to rue a sloppy end to the match in which his team missed several opportunities while also letting in Coutinho for what proved to be the winner.
He said: "We had clear chances to score in the last 15 minutes but we made a mistake and they won the game.
"They started very well and scored two goals. It's easier when you are playing at home and go two goals in front - it's more easy to play with calm.
"After that we rearranged things, had two or three clear chances at the end of the first half and then we scored two goals.
"But we made that mistake and they win the game."