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City's 2-0 victory at Roma on Wednesday allowed them to secure an improbable place in the last-16 of the Champions League after they had failed to win any of their first four group games.
But it is defending the Premier League title that is now top priority Pellegrini.
The City manager is determined to keep the pressure on leaders Chelsea, who are only three points clear of the champions after losing their unbeaten record at Newcastle last weekend.
"The most important thing now is to switch. We have finished with the Champions League and don't have to worry about that until February," said Pellegrini ahead of Saturday's trip to bottom of the table Leicester.
"We have to play four more games in the Premier League in December which are very important to try to continue to count points up on Chelsea.
"We have 12 more points in December and that's what our minds must be focused on 100 per cent."
City will have to try and get those points without leading scorer Sergio Aguero, who is out for between four and six weeks with a knee ligament injury, while captain Vincent Kompany could also still be missing for the Leicester clash.
But they managed to beat Roma without Aguero, who has scored 19 times this season, and Pellegrini has been at pains to point out that City are not a one-man team.
"The same as Cristiano Ronaldo at Real Madrid and Lionel Messi at Barcelona, Sergio is a very important player," Pellegrini said.
"But we are not just one player. We are an important team with good players."
- Back to their best -
City will look to maintain their winning run at Leicester before facing Crystal Palace, West Bromwich Albion and Burnley – who are all in the Premier League's bottom six – over the Christmas period.
And City defender Gael Clichy believes the team are finally getting back to their best following an indifferent start to the season.
"In the last three or four weeks we have seen the real side that won the Premier League last year," he said.
"When we play like this we can only be confident and hopefully we can do great things this year.
"I think we are improving. It was about time, because in the first part of the season we did not play well.
"We have to forget what we did on Wednesday by keeping in mind we have the quality and if the focus is there I think it's hard for any team to win against us."
Meanwhile, Leicester manager Nigel Pearson has been charged by the Football Association with using abusive and/or insulting words to one of his own supporters in an outburst during the recent 3-1 home defeat by Liverpool.
And to make matters worse, Leicester's former City goalkeeper Kasper Schmeichel this week broke a metatarsal (foot bone) in training.
The Denmark international, 28, was due to face surgery on Friday with Pearson admitting he would be out for at least a month and possibly even longer depending on the outcome of the operation.
"Kasper will be having an operation tomorrow on a metatarsal he broke this morning," said Pearson, whose side have gone 10 games without a win.
"It's very unfortunate and clearly the lad's distressed about it. He will be a big miss for us. We have to deal with it. We can't change it.
"An optimistic view would be four-six weeks but it could be longer. We don't know. It will depend very much on what the surgeon finds."