Philippe Coutinho struck a crucial winner as Brendan Rodgers' side emerged 3-2 victors, a result which puts Liverpool's title chances firmly in their own hands.
Liverpool will end their 24-year wait for a league title if they win their remaining four matches, but Pellegrini has challenged City to apply as much pressure as possible.
|MAN CITY LATEST
|11/5||Man City are 11/5 with Bet365 to win the title this season|
The 2011-12 champions host Sunderland on Wednesday in the first of two games in hand they hold over title rivals Liverpool and Chelsea, with Pellegrini confident his players will need little motivation going into the game.
"I think the team knows perfectly what they have to do," he said.
"We lost that game [at Liverpool] but we have still to play six games more and we will fight to the end to win the title.
"If we don't do it, it is because Liverpool will win their four games, but I don't think some things change after the game on Sunday.
"Of course, the fans believe that we can do it. The two games postponed - if we win both we are just one point behind Liverpool.
"If you don't believe [when you are] just one point behind the leader, nobody can believe anything.
"We have had a very good season so far and we hope we finish in the last six games in the same way."
Pellegrini will not have the services of Yaya Toure for the visit of relegation-threatened Sunderland, and expects a tough test as Gus Poyet's side scramble for points.
"I think that playing against a team in relegation trouble, that's a very difficult position," he added.
"Sunderland will have to play six games and the others four games so nobody can think that any one of those games will be easy.
"We play here at home, they are in a difficult moment, but I am sure that we will try to fight until the end to continue in the Premier League."