City secured their passage into the last eight thanks to a controversial penalty winner from Elano with five minutes to go.
The spot-kick was awarded after substitute Lubomir Michalik was adjudged to have handled the Brazilian's cross.
Bolton manager Megson said: "You have got to be 100% certain if you are going to give a penalty at that stage of the game. I cannot see how he could even be 50% sure.
"It was not clear cut. It was a bit of a nonsensical decision in such an important game.
"The lad cannot get out of it even if he tried and it has obviously cost us dearly. But the players deserve great credit for keeping going."
Sven Goran Eriksson was relieved that his side were able to bounce back after the defeat by Chelsea.
He said: "The spirit was there again and we defended very well, even in the last 10 or 15 minutes when Bolton put a lot of players up.
"It was important to go through and reach the quarter-finals. I am happy about that.
"I thought it was a penalty. The player moved his arm but whether it was intentional I do not know.
"I can understand Bolton being upset about it. These decisions it is very difficult to say whether it was right or wrong. But the linesman was close to what happened.
"Elano remained cool to take the penalty and showed his experience."