UEFA said on Friday its protocol for match officials to handle racism incidents "was not applied" during the CSKA Moscow-Manchester City match on Wednesday.
"This protocol empowers the referee to stop the match and ask for a public address system announcement to be made urging spectators to stop such racist conduct," UEFA said in a statement.
Platini's request puts 33-year-old Romanian referee Ovidiu Hategan under scrutiny as well as the Russian club.
UEFA has opened a disciplinary case against CSKA, prompted by complaints by City and midfielder Yaya Toure, who is black.
Toure said he told Hategan during play about monkey noises being targeted at City's black players by home fans.
"UEFA must take their decision about that," City manager Manuel Pellegrini said on Friday of Platini's request. "We did all that we can do here, we can't do any more."
Hategan, who has been a FIFA international list referee since 2008, did not stop play and ask stadium officials to broadcast a warning. It is the first step of UEFA's guidelines to deal with racist abuse in stadiums.
If abuse continues, the second step in UEFA's protocol empowers referees to suspend a match and take teams off the pitch. The third is abandoning the match.
UEFA said it will publish its investigation findings after the disciplinary case next Wednesday.
Russian football authorities on Friday declined to condemn CSKA, the defending champion.
The Russian Football Union said "CSKA fans have always been known for their loyalty to the club and proper behaviour at arenas," in a statement which expressed support for FIFA and UEFA efforts to tackle racism.
Russian league chief executive Sergey Cheban, who attended the match at Khimki Arena, told The Associated Press "there was not an incident."
"Maybe a misunderstanding. The stadium is relatively small. The acoustics are very special in there as well. So maybe just a misunderstanding," Cheban said through an interpreter at a meeting of European leagues in Paris.
The incident has directed attention at Russian football's issues with racism ahead of the country hosting the 2018 World Cup.
The 2012 European Championship in Poland and Ukraine raised the profile of UEFA's guidelines for referees, who have had authority since 2009 to halt matches and deal with racist abuse.
UEFA insisted ahead of Euro 2012 there was a clear protocol in place after Italy forward Mario Balotelli, who is black, suggested he would walk off the pitch if targeted for abuse.
CSKA has questioned whether any racially motivated abuse was used, even as it issued a statement on Thursday regretting the incident.
"Having carefully studied the video of the game, we found no racist insults from CSKA supporters to the guests," the club said.
CSKA has increasing influence in European football through its director Evgeni Giner.
Giner sits on the Platini-chaired UEFA strategy council, as one of four delegates representing European clubs. Giner also sits on UEFA's club competitions committee which makes key recommendations about running the Champions League.
AP Sports Writer John Leicester in Paris and Associated Press writer Vladimir Isachenkov in Moscow contributed to this report.