"I think everyone has the right to boo or protest on different things," Pellegrini told reporters ahead of Tuesday's return game in Spain.
"If they boo then they feel there's something UEFA is not doing right."
The Chilean's comments come in the wake of club captain Vincent Kompany describing UEFA's investigation as "a joke".
"There is nothing holy about the Champions League anthem," the Belgium defender had said.
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We have played many games in Europe where there has been racial abuse -- we have had to put up with it."
City's fans are frustrated with UEFA over the organisation's decision to play a Champions League match against CSKA Moscow behind closed doors last year because of a series of offences, including racial abuse, from the Russian club's fans.
City supporters who paid to travel to Moscow for the game were not compensated by UEFA, while some CSKA fans were reported to have attended the fixture.
City supporters are understood to have regularly booed the Champions League anthem over the past year.
UEFA's disciplinary body will consider the case against City on Nov. 19 and a charge could follow.
(Reporting by Simon Jennings in Bengaluru; Editing by John O'Brien)
