City secured a place in the last 16 for the first time as they crushed CSKA Moscow 5-2 at the Etihad Stadium.
Alvaro Negredo claimed a hat-trick and Sergio Aguero also struck twice as City made sure of at least second spot in Group D.
When asked if the performance provided evidence City could trouble any team, Pellegrini said: "I think so but, at this level, also every team can beat us.
"There are some important teams in Europe but I think we have a strong squad and we'll see where we can go in this Champions League."
The result was not in doubt after Aguero hit his first in the third minute from the penalty spot after David Silva was fouled.
He added a second after 20 minutes and Negredo made it 3-0 after half an hour.
Seydou Doumbia pulled one back and also scored a penalty after Negredo had tapped in his second early in the second half.
But they were rare interruptions to City's flow and Negredo headed his third in the final minute.
After failures in the group stages in each of the past two seasons, the result was highly significant for City as they look to make an impression on the European stage.
Pellegrini said: "We're very happy because it is an achievement for the club.
"We didn't do it in the last two years - it's not easy to do it.
"Two games before the group is finished and we are in the round of 16. I think it is very important for the players, the fans, the whole club.
"I don't know if it's a relief but it was our first target this year and also to be in that state is important for the club."
Pellegrini hailed his strike force of Aguero and Negredo, who between them have now scored 22 goals this season.
He said: "Both played very, very well - and not only today but all season.
"Aguero is in a great moment, not only because he's scoring, but whole team is playing in an offensive team and that's important.
"We scored five goals and had five or six chances more."
City midfielder Yaya Toure, who was the victim of the racist chanting from CSKA fans that soured the first meeting between the clubs a fortnight ago, paid tribute to his side's supporters.
Toure told Sky Sports: "It's amazing, I think it's deserved by the club.
"We go through to the second round for the first time and it's unbelievable.
"I thought we played amazingly well today and we have to say thank you to the fans as well. They showed to the fans of CSKA how supportive our fans are.
"It was very nice to win today, it was very fantastic.
"We are happy with the win today and I think today is a special day for the fans and for the club as well."
CSKA boss Leonid Slutsky blamed his side's own shortcomings for the defeat rather than City's attacking brilliance.
The Russians were beaten 3-0 by Bayern Munich in their first game of the campaign and Slutsky compared City unfavourably to the German giants.
He said: "We made a lot of mistakes. Obviously we were playing against players of a high level, but those mistakes were our fault.
"We lost because of ourselves, while in Bavaria it was mostly down to the level of the other side.
"How can you be psychologically ready when after the first minute you concede a goal and then three goals during the first half?
"There was a lot of freedom to attack but we were unbalanced in defence.
"Obviously when we had chances we scored but we should be quite alert.
"With such a tough team as Man City you have to be alert because they can be fatal in a split-second."