City have never made it out of the groups in their previous two attempts, but under Pellegrini they have swept into the last 16 and they completed their qualification with a 5-2 hammering of CSKA Moscow on Tuesday.
Now the Chilean firmly believes that City are a match for anyone in Europe.
"I think we can beat any side now, when we play at our best," Pellegrini said.
"I think the most important teams in Italy, Spain and France are competitive, so we will see where we go now.
"We have a strong team and the minimum target was to qualify for the next round, but it is not our only target.
"We have a strong squad and we will see who we will play in February, but I can assure you that, whoever we draw, they will not be very happy to play against us."
Pellegrini admits City making it through the group stage is a big step for them.
"We are very happy because this is an achievement in the history of the club," Pellegrini continued.
"You can see from the last two years it is not easy, and yet two games before the end, we are in the round of 16, and that is great for the fans and the whole club.
"For now, of course we are going to try and top the group. It is important to try and do that, and we will keep trying to the end to get above Bayern."