Liverpool defeated Debrecen 1-0 but failed to qualify for the Champions League knockout stage as Fiorentina secured the last qualification spot in Group E with a victory over Lyon on Tuesday.
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"I'm very disappointed because we had chances in all the games," said Liverpool manager Rafa Benitez. "We have to be disappointed but at least we won. We did our job today."
David Ngog scored in the fourth minute, his tap-in from three meters deflecting in off the post after Jamie Carragher headed the ball back across the box.
Liverpool had several other chances, with Debrecen goalkeeper Vukasin Poleksic making good saves from Ngog in the 38th and Steven Gerrard in the 59th.
Benitez lamented that late goals suffered in earlier group games had undermined Liverpool's campaign.
"We were not worse than the other teams," Benitez said, adding that Liverpool would now concentrate on Sunday's English Premier League match against Everton and later on the Europa League, for which it qualified courtesy of its third-place finish in Group E.
Despite the defeat, Benitez found solace in Gerrard's return from injury and the England midfielder's good form during the match.
"He can now play more or less 90 minutes," said Benitez, who sent Alberto Aquilani on for Gerrard with just seconds left in the match.
Gerrard, who scored crucial goals in Champions League victories for Liverpool in past seasons, was unable to convert against Debrecen.
