Uefa punished the Russians after Yaya Toure was subjected to offensive chanting during the reverse fixture and the Manchester City boss is now keen to move on
CSKA's next home Champions League match will take place with part of their stadium closed after Uefa punished the Russian club for the abuse Toure suffered during last month's meeting with City in Russia.
The two teams meet again in Manchester on Tuesday, with Pellegrini hoping lessons have been learned by the CSKA support.
"The fans of CSKA made an important mistake," the Chilean told reporters. "I don't know why CSKA denied it at the beginning; I don't know what their reaction is now.
"Uefa acted and gave them the punishment it deserved. Hopefully we can leave this in the past. Hopefully it will be an example for Russian fans because they have a World Cup in their country."
Pellegrini confirmed injured duo Vincent Kompany and Stevan Jovetic will miss Tuesday's Group D clash with CSKA, while Costel Pantilimon will be preferred in goal to Joe Hart once again.
Hart was dropped for Saturday’s 7-0 victory over Norwich after making a string of mistakes, but Pellegrini has praised the response of the England No.1.
"Joe has reacted very well," he added. "For him this is a good thing after playing so many matches over the past two or three years.
"He has been working no problem, supporting Costel. Nobody wants to be out but he thinks a rest will be useful for him too."