Coins were thrown when David Faupala celebrated with City teammates in the corner of the pitch, near Chelsea fans, after scoring on his debut.
"We condemn such idiotic and dangerous behavior," Chelsea's head of communications, Steve Atkins, said. "If we can identify those responsible, then we will ban them from Stamford Bridge.
"It is worth noting it is a criminal offense, too. We will support any police prosecution if we can identify, along with the police, the individuals responsible for their behavior today."
"I was aware. I can easily say 'no, I am not aware' - but I was aware," Hiddink said. "I like to always face the facts. "There were coins thrown to the Man City players in their celebration. We condemn it, I condemn it strongly and Chelsea, I think they will react. Those people, they must not come into stadiums."
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City manager Manuel Pellegrini said he did not know about the incident in the 37th minute of a game which Chelsea eventually won 5-1.
On Saturday, West Bromwich Albion captain Chris Brunt was struck in the face by a coin which was thrown by a supporter of his team after a 3-1 defeat by second tier Reading. Brunt had gone over to applaud the fans for their support at the end of the match.
The English Football Association is investigating the incident involving Brunt.
"We strongly condemn any such behavior and will work with both clubs and the authorities to identify those responsible," the FA said in a statement.