City's unconvincing 1-1 draw with Roma at the Etihad Stadium on Tuesday has left them with just one point from their opening two fixtures in Group E.
The Barclays Premier League champions are now already five points behind group leaders Bayern Munich and again face a familiar battle to qualify for the knock-out stages.
City's next two games against CSKA Moscow away and at home are likely to be critical to their hopes of making progress.
Asked in his post-match press conference how difficult it would now be to qualify, Pellegrini said: "We don't know
It depends on the way we play the next game.
"We have just one point from six but also we are just three points behind Roma, so there is a lot of things (to play for)
We hope next game in Russia we can win and we will see what happens against Bayern Munich.
"We have 12 more points to fight (for) and we will fight to the end to try and qualify."
City took an early lead as Sergio Aguero struck from the penalty spot but Roma were superb in attack and pushed the hosts onto the back foot.
Their 23rd-minute equaliser, through 38-year-old Francesco Totti, who in the process became the Champions League's oldest goalscorer, was sublime and deserved.
Roma continued to press and although City finished the stronger, they were fortunate not to concede again.
Pellegrini, whose attacking philosophy is well known, played down suggestions he might have been taken aback by Roma's bold approach.
The Chilean said: "It was not a surprise for me
They are a team in form with great players
They made it difficult for us, it was a difficult game but I thought we could win it in the last 20 minutes.
"A point playing at home is never good but we played against a very strong team in a very good moment (of form).
"We didn't play well, especially in the first half
We improved in the second half but I think the draw was the real (right) thing for both teams.
"We must continue fighting for the next 12 points and we will see which teams qualify for the next round."
Pellegrini refused to single out any players for blame for the equaliser, which Totti finished with a superb flick over Joe Hart after being afforded plenty of space.
Pellegrini said: "I think that when the other team scores a goal it is not just a problem of one or two players
I think that he had too much space in that play.
"Maybe it was an easy goal for them but you must have the quality and the capacity to return to your normal performance
Today was not our day."
Roma's former England defender Ashley Cole, who was playing his first match back in his homeland since joining the Italian club, hailed the visitors' performance.
The former Chelsea left-back told ITV: "I think it was a good performance from the boys after going 1-0 down so early in the game and we showed a lot of character, determination and belief in the team.
"Maybe we should have won but the boys can be proud of themselves for going up against the (Premier League) champions, a great team.
"We're probably a bit disappointed we didn't win but it's a good point for us."
Coach Rudi Garcia, who has overseen a fine start to the season with five straight Serie A wins, felt his side had made a statement.
He said: "We have shown we are at the height of this group
We have played against the champions of England, one of the richest clubs in the world and it wasn't easy to start off one goal down.
"We have a good team and took advantage of our good moments."
On Totti's landmark strike, Garcia said: "I took great pleasure in the goal today."
Source : PA
Source: PA