Having demolished Norwich City 7-0 in the Premier League on Saturday, City have now scored 12 goals in their last two matches.
Alvaro Negredo led the charge against CSKA on Tuesday with a hat-trick, while Sergio Aguero claimed a brace as City qualified for the knockout rounds after successive group-stage exits in 2011 and 2012.
Asked if City could beat any team in the competition, Pellegrini replied: "I think so. But at this level, every team can beat us also.
"There are the most important teams in Europe, the most important teams in Spain, in Italy, in France. I think we have a strong squad and we will see where we can go in this Champions League."
After hosting Group D's bottom side Viktoria Pilsen on November 27, City will conclude the group phase away to defending champions and pool leaders Bayern Munich.
Bayern currently lead City by three points, but Pellegrini believes that regardless of the final standings, no team will relish a trip to the Etihad Stadium in the round of 16.
"The minimum target was to qualify for the next round, but it wasn't our only target," he said.
"We must continue in Europe. We will see the draw, because we don't know with whom we are going to play in February, but I am sure that the team we play against will not be very happy to play against us."
CSKA will play host to Bayern in their next game with part of their stadium closed as a punishment for the racist chanting to which City midfielder Yaya Toure was subjected when he played there two weeks ago.
Tuesday's reverse fixture passed off without off-field incident and afterwards, Toure made a pointed reference to the conduct of his side's supporters.
"We must say thank you to the fans today," said the Ivorian. "They showed the fans of CSKA how to support a team."
When CSKA coach Leonid Slutsky was asked in his post-game press conference whether anyone from his club had spoken to Toure about the incidents in Moscow, he replied: "I don't know."
Pellegrini urged CSKA's supporters to learn their lessons from the affair.
"I think maybe if the fans of CSKA will have another way to support their team, I think that's the better way," he said.
"They have to have another way to support their team. UEFA made the thing (punishment) that they had to do and it's better to finish with that thing."
While Negredo and Aguero took most of the plaudits with their goals, Pellegrini was also eager to underline the contributions of attacking midfielders Samir Nasri and David Silva, who tormented CSKA throughout.
"Both of them, Silva and Nasri, are two very important creative midfielders and they play really well," said the Chilean.
"I think also that the way we are playing, giving both of them the freedom to play where they want, with all the movement, is also important for both of them.
"For the two strikers, with the way we play, trying to always be in the opposite side (half), it allows both of them to play very well with the ball at their feet. It's a mix of all."
Slutsky, whose side can no longer qualify for the last 16, attributed Tuesday's result to his own players' mistakes and said he had been more impressed by Bayern, who beat CSKA 3-0 in their opening group game.
"Obviously we were playing against players of a high level, but the mistakes were our own," said Slutsky, whose side scored twice through Seydou Doumbia.
"We lost because of ourselves, whereas in Bavaria (against Bayern Munich) it was mostly down to the level of the other side."
