After a good opening by City, the Bundesliga leaders took control and were ultimately good value for their victory.
Manager Jupp Heynckes said: "We chose the right time to score and then played very confidently.
"At the beginning of the game we were nervous and we did not do ourselves justice.
"We changed midway through the first half and came into the game.
"Franck Ribery has given a world-class performance, Bastian Schweinsteiger also.
"In the second half we played as a unified team.
"At the moment we have not only a great team spirit, but also act in harmony, a good foundation and outstanding individuals."
Chairman Karl-Heinz Rummenigge concurred, saying: "This was a very good game from us. Manchester City also played very well in the first 30 minutes to show that they are a strong team.
"We played mainly in the second half, totally in control. It was a great team performance, with Franck Ribery and Jerome Boateng playing really strong."
Goalscorer Gomez said: "Manchester ran the ball well at the beginning.
"We were perhaps a little nervous, which is really inexplicable, because we are actually in a good phase.
"As a team we have from the 30th minute done well and ultimately deserved to win.
"I have not played outstanding, but scored two goals."
The positive mood at the Allianz Arena was contrasted by the chaos in the City camp after Carlos Tevez refused to come on as a substitute in the loss.
Edin Dzeko was replaced by Nigel de Jong in the second half of the Champions League Group A match and soon after the City boss asked Tevez to warm up, but manager Roberto Mancini claims he refused to do as he had been asked.
"He just refused to go on. I don't know why," said Mancini.
"I cannot be happy with this situation. Would something like this happen at Bayern Munich, AC Milan or Manchester United?
"I am the manager. I decide everything.
"I have helped him every time for two years, he has wanted to leave but I still picked him.
"The thing is there were still 30 minutes until the end of the game. We could still change it.
"Carlos didn't play at the start of the season because he has not had a pre-season for three years. He was not ready to play.
"If it was another player may be this could happen but for a player to refuse to go on in an important game like this is not right."
This would have been bad enough had it been the only problem Mancini had to deal with.
However, there was also the problem of striker Edin Dzeko shaking his head at Mancini as he was replaced by Nigel de Jong 10 minutes into the second half.
It was that change that angered Tevez, who was left on the bench throughout his side's Barclays Premier League win over Everton on Saturday, and it appeared Dzeko was equally annoyed.
"He was disappointed but he played a bad game," said Mancini.
"I wanted to keep the score down and not concede a third goal.
"It is the last time any player at this club does that."
Amid the carnage, City were fortunate their defeat was contained to just two first-half strikes from Mario Gomez.
It could have been far more. But the aftermath will be dominated by Tevez and assistant manager David Platt insists Mancini is the right man to deal with it.
"We are not going to lie. What happened happened," said the former England skipper.
"Roberto will sleep on it and look at it and dealt with it in the way he sees fit."