Premier League - City take third with win at Bolton
Arsenal finished fourth in the table after a 2-2 draw with Fulham at Craven Cottage. They will be forced to play a qualifier if they are to reach the group stages of the world's biggest club competition.
City defender Joleon Lescott did not know much about the fortuitous goal that opened City's account in the 43rd minute.
Substitute Edin Dzeko netted with his first contribution of the match on 62 minutes to condemn Bolton to a fifth straight defeat.
The win completes a successful season for City.
They won the FA Cup and finished third in the table under Mancini, who must wait to see if Carlos Tevez will be part of his squad next term with the Argentina forward set to return home to discuss his future with his family.
Kevin Davies missed a couple of decent chances with headers before Barry somehow contrived to hit the bar with a free header from two yards out after an energetic run and cross from Dedryck Boyota on 34 minutes.
Jasskelainen was forced to claw out efforts from Yaya Toure and Tevez as Silva trashed the rebound over the bar as the Bolton goal led a charmed life before Lescott struck the opener.
With Arsenal twice trailing at Fulham, City were always well in control of their own destiny knowing a win would secure them the third place they craved.
Gary Cahill had a volley charged down by a posse of home defenders early in the second period, but City sealed the three points with a move of genuine quality.
Boyota fed Tevez, who supplied a wonderful little pass to Barry. His cross fell kindly for Dzeko from the unfortunate Cahill, and he wasted little time in hammering the ball into the net for his second goal in the Premier League.
City were never under any threat after that with Jaaskelainen forced to make fine saves from Tevez to prevent the day going from bad to worse for Bolton, who finished the season in 14th place - the mirror image of a year ago.