After drawing the first leg 1-1 in Turkey, Galatasaray knew they had to score at least once to have any chance of progressing to the quarter-finals but they put in a limp display at Stamford Bridge.
Even striker Didier Drogba, the subject of much of the talk in the build-up ahead of his return to his former club, failed to cause any problems for the home defence as first-half goals from Samuel Eto'o and Gary Cahill saw Chelsea through 3-1 on aggregate.
Mancini and opposite number Jose Mourinho did little to hide their dislike of each other leading up to the game but it will be the Portuguese who will come away much the happier after getting the better of his counterpart.
The Italian was left to rue his side's poor performance, conceding that Chelsea were worthy winners.
"We really played very, very badly," he said after the match.
"Chelsea were the better side and they converted the opportunities they got.
"It’s impossible to score with just one shot on goal. We need to take several steps in order to be a better team."
Drogba, meanwhile, was disappointed with his side's inability to match their first-leg performance.
"We wanted to play the way we played in the first leg but that did not happen," the Ivorian striker said.
"We are still learning and the team is still young. I hope next season things will be different."
