Both teams won their opening fixture 4-0 and remained committed to scoring goals in an engaging display of attacking football.
Yet City manager Roberto Mancini was far from pleased following the contest as he believed his side had gifted Bolton its goals to make the game unnecessarily tense.
He is also concerned about whether he will be able to sign Samir Nasri from Arsenal before the London club's Champions League second leg against Udinese on Wednesday.
If Arsenal manager Arsene Wenger plays Nasri in that match then he will be ineligible to play for City in the same competition should a move go through.
"I hope that we can have Samir Nasri in the next day," Mancini said. "But I don't know when. We still have 10 days. We need some players if we want to complete our team. I hope he (Nasri) is not the last one in. If he plays in the Champions League, it is a big problem. I don't know (if I would still sign him) but hopefully we will close in the next 24 hours.
"We need to pay more attention. We cannot afford to concede these goals and we need to pay more attention on this if we want to be a good team. I think that first six or seven games in the season are strange, but I think that maybe this year we can maybe score more goals than last year. We dominated the game, so it should be impossible that the game can still be 3-3 in the 90th minute."
In an enthralling contest, Silva benefited from Jussi Jaaskelainen's goalkeeping error in the 26th minute to give City the lead, before Barry doubled the advantage with a long-range effort in the 37th.
Ivan Klasnic immediately responded to give Bolton hope, but Dzeko's early second-half strike restored City's two-goal cushion.
Kevin Davies again breathed life into Bolton's afternoon as he headed in Paul Robinson's delivery in the 63rd, but the hosts couldn't pull off a further comeback.
"City have assembled a terrific team and you have to give credit where credit is due," Bolton manager Coyle said. "It would have been easy to feel sorry for ourselves at 2-0 down and 3-1 down, but we fought positively and that is what we will take from the match.
"We probably gifted them one or two of the goals, and if one of the top clubs is going to beat you then make them earn it."
