The police and the Football Association are both looking at the incident.
Asked if the club would take any action against Bellamy, City's assistant boss Mark Bowen told BBC Radio 5 live: "No. I don't think there is any need to.
"My take is that he thought the fella might spit in his face or something," added Bowen.
"He came very close and moved towards him. Craig, with an open hand, just pushed the fella away."
City manager Mark Hughes has also defended Wales captain Bellamy's actions, saying: "I did not see it but the guy should not have been on the pitch. That is not acceptable."
Greater Manchester Police have charged the supporter for entering the playing area "without lawful authority".
In a hotly-contested derby battle, the Blues came from behind on three occasions with Bellamy scoring two magnificent goals, including an equaliser to make it 3-3 in the 90th minute.
"Brian Clough clipped someone's ear," added Hughes. "He was lauded a national hero. Maybe it'll be the same with Craig but I doubt it."
Earlier, an FA spokesman said: "We are investigating the incident and we will be looking at the referee's match report."
Disciplinary officials have already seen TV footage of the incident and the FA is likely to make a decision on whether to charge Bellamy later this week.
Former Manchester United defender David May believes the emotions of the situation had an influence on Bellamy's reaction to the fan.
He told BBC Radio 5 live: "It was silly but I suppose to a certain extent it was understandable.
"When anyone comes on to the pitch it's worrying but maybe he shouldn't have slapped the fan, he should have walked away and let the steward get on with it.
"Players have to be professional but I think the whole occasion got to him - he had got City back into it at 3-3 and his emotions were running high.
"But you can't go round slapping fans. It's the wrong thing to do."
City boss Hughes also confirmed substitute Javier Garrido was struck by a coin thrown from the home section of the stadium at half-time.
It is likely that former United hero Carlos Tevez had been the target as he was standing near Garrido when the coin was thrown.
The Argentine, who moved across to Eastlands in the summer, was booed throughout the match by some of the home supporters.
Garrido was not hurt, but the Football Association could be called upon to pass judgement on the two incidents.
"Something came from the crowd but he is OK," Hughes added.
City striker Emmanuel Adebayor is already facing an FA improper conduct charge after running the length of the pitch to celebrate in front of Arsenal supporters after scoring against his former team.
The Manchester United fan who came on to the pitch after Michael Owen's late goal is set to appear in court later this month.
A Greater Manchester Police spokeswoman said: "A man has been charged following an incident at the end of the match between Manchester United and Manchester City at Old Trafford.
"Jake Joseph Clarke, 21, is charged with going onto a playing area without lawful authority or excuse and will appear before Trafford Magistrates' Court on September 30."