Terry and Frank Lampard, who jointly lifted the cup in Munich last May, handed the silverware over to UEFA president Michel Platini in a symbolic ceremony in London.
Chelsea are in the running for continental honours after reaching the last four of the Europa League - but it is Champions League football they crave.
To secure place among elite, Chelsea, currently third, must retain their place in the top four of the Barclays Premier League.
Terry said: "To hand it back has been very sad. It is a trophy we worked so hard for.
"To come here and hand it back not even a year on has made us doubly determined to cement our place in the Champions League for next season.
"The players are happy where we are in the league at the moment. To be able to strengthen and keep the existing players we have got, we have to cement that."
Terry denied he had contradicted Chelsea's interim manager Rafael Benitez, who had cast doubt over his fitness after a season disrupted by a knee injury.
The defender said he accepted Benitez's rotation policy but would always be available to play.
"There has been a lot made of it. Even today. I didn't speak out against the manager at all. I am fit, I have been fit," Terry said.
"There is nothing to read into it. If the manager chooses not to play me that is his preference and I have no qualms about that because the two or three guys in front of me are world-class players.
"It is down to me to work hard, do my best on the training field and, when selected, do my best for him.
"I am Chelsea's biggest supporter, whether I am playing or not playing."
Terry is heading into the final year of his current Chelsea contract and he would be keen to sign another one.
"Of course, I love Chelsea. This is my club," he said.
Chelsea chief executive Ron Gourlay refused to discuss the club's search for a new manager for next season.
Asked whether Benitez had a chance of being retained if he met his targets of winning the FA Cup and finishing in the top three, Gourlay said: "We will look at everything at the end of the season.
"We were clear the role was interim until the end of the season and we will sit down then take it from there. We have to believe we can deliver the points."