The Premier League champions will need to pull off a surprise fightback at Camp Nou next month if they are to qualify for the UEFA Champions League quarter-finals after they were beaten 2-1 at home.
It could have been worse for City, who were indebted to Joe Hart for saving a last-gasp penalty from Lionel Messi to give them hope in the second leg.
City must now ensure their week does not go from bad to worse on Merseyside, where they will have an opportunity to cut Chelsea's lead at the top of the Premier League to only two points as the leaders face Tottenham in the League Cup final.
Liverpool beat City 3-2 at Anfield last April to take a giant stride towards winning the title, only for Brendan Rodgers' side to slip up and open the door for Pellegrini's men to be crowned champions.
You have to go back May 2003 for City's last victory at Anfield and Pellegrini has stressed the importance of ending that dismal 12-match run this weekend.
The former Malaga coach said: "You must change it. This year we won at Stoke. In the last six years we never did that."
Liverpool are also licking their wounds following the disappointment of Thursday's Europa League exit at Besiktas on penalties.
And Pellegrini wants City to make the most of their opponents coming into the game on the back of a clash in Turkey only three days earlier.
He added: "Of course it is an advantage but not a decisive one because I always think the decisive thing is the performance on the day of the game.
"But I have played in the Europa League and when you arrive on Friday it is not the best way to prepare for a game on Sunday but that is the rules.
"If we think we are going to win that game because Liverpool arrive yesterday night late, that is not the reason. We must play very good because they also have a strong squad. I don't think they will play the same starting XI as yesterday night."
City will welcome back Yaya Toure from his European suspension and Pellegrini has no injuries to contend with.
Playmaker Philippe Coutinho is expected to return to the Liverpool side after being rested on Thursday, while Lazar Markovic is back in contention after missing the Besiktas defeat due to a European ban of his own.
Liverpool, unbeaten in 10 Premier League games, will check on the fitness of captain Steven Gerrard (hamstring), Jordan Henderson (ankle), Mamadou Sakho (hip) and Glen Johnson (illness).
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