The Biancocelesti, trailing 2-0 from the first leg and playing in front of an empty Stadio Olimpico following repeated episodes of racist behaviour from supporters, took the lead through Senad Lulic.
But hopes of a dramatic comeback were dashed when Caner Erkin equalised and ensured Fener prevailed 3-1 on aggregate, though Petkovic was quick to hail his team after the game.
"The qualification was already compromised by the match. But, I'm very happy with the team we tried right to the end despite qualification becoming impossible," he told Sky Sport 24.
Lazio enjoyed the better of the possession on the night and applied concerted pressure on the Fenerbahce goal in pursuit of a route back into the tie, and Petkovic admits his team should have been more ruthless.
He added: "There is regret because we had 15 shots on goal but we lacked precision. Now, we have to regain energy for the match against Juventus, we want to fight for the third place."
Petkovic then gave his thoughts on playing in front of empty seats and admitted that the absence of supporters was a big blow to his side's chances of overturning the aggregate deficit.
"With a better draw we could have gone further. My considerations are the absence of the public, who at 1-0 would have given us the right push. I hope we never have to play without them again."