Midfielder Yaya Toure was abused by a portion of the Russian fans in October, with the home side ordered to partially close their stadium for their next European fixture despite hitting out at the Ivorian's claims.
"The fans of CSKA made an important mistake," Pellegrini told the press. "I don't know why CSKA denied it at the beginning; I don't know what their reaction is now.
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The English side come into the game holding second place in Group D, three points behind Bayern Munich and three ahead of the Russian club after winning 2-1 at the Arena Khimki, and the Chilean wants his men to repeat the result as a step towards fulfilling their aim of reaching the knockout stages.
Pellegrini declared: "We have a very good squad and the minimum we need to do is to qualify for the next round.
"It is not very easy to talk about what might happen in the future but [on Tuesday] we will try to make that first step and after we will think about the rest. At the moment, we just need to focus on [this game].
"CSKA have a lot of very good players. We played a very close game there in Russia and I think [Tuesday] will be the same."
Defender Pablo Zabaleta agreed that CSKA would provide a tough test but is well aware his side need to do well after struggling in Europe over recent seasons.
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"We had a great win against Norwich [on Saturday] but now it's time to think of the Champions League, where we have a great chance to win [against CSKA]. Hopefully we can have a good game and to try and get three points is very important to us.
"We haven't had a great record in the Champions League but we've been very focused to try to improve our performance in the competition.
"It takes time. We've won the FA Cup and the league, and the Champions League is against some of the best teams in Europe, but I think we are ready to take a big step forward. Hopefully, in the next few years, we can be one of the top teams in Europe."