Title favourites City were knocked off the top of the Barclays Premier League as they were thrashed 4-1 by the Merseysiders and Pellegrini wants a reaction against Juventus on Wednesday.
City are in Turin this week for their penultimate Champions League Group D game and, although they have already qualified for the last 16, they want to secure top spot.
Pellegrini said: "I think that we finished with the game - that very bad game that we played on Saturday - on Sunday morning.
"This is a different competition and a different game
We are thinking of playing here against Juventus at home and trying to beat them.
"It was a strange and fake game that we played, and that is the past
It is more important to think about the future
I hope we will return to our normal performance."
City have won their last three matches in the competition to secure their place in the knockout stages with two games to spare.
The first two results in that sequence came courtesy of last-gasp winners but Pellegrini's men were highly impressive in their last outing away at Sevilla.
Pellegrini hopes that has provided a blueprint for the future as City look to progress beyond the last 16 for the first time and transfer some of their domestic dominance to the European stage.
The Chilean said: "I think first of all we need to play in Europe in the same way we did against Sevilla.
"We have a lot of experience now, better than the other years
We need a performance in these games.
"We have qualified for the last two years
This year it is important to try to be at the top of the group, not only to avoid Barcelona or other important teams but because it is a test for us to try and win in a difficult stadium here."
City will again be without influential captain Vincent Kompany due to a calf injury and his fellow centre-back Eliaquim Mangala is also unavailable due to an unspecified problem.
With playmaker David Silva and striker Wilfried Bony still not ready to return from ankle and hamstring injuries, and Pablo Zabaleta and Samir Nasri sidelined, City are short of senior players.
Pellegrini accepts that makes for a "difficult situation" but is still determined to put in a strong performance.
City lead the Italians by a point and will secure first place with a win
Juventus will guarantee their progress with a victory, but a defeat could even be sufficient if Sevilla do not beat Borussia Monchengladbach in their game.
Pellegrini said: "We have played already against Juventus
It was a very close game, we did not deserve to lose.
"They are not in their best moment here now in domestic football but I am sure we will find a team who wants to qualify first in the group
I hope they find a Manchester City team who will fight for the game."
Source : PA
Source: PA