An uncharacteristic 61st-minute blunder from Reina – who claimed to have been bothered by a laser pen in the crowd during the first half – saw the goalkeeper allow a tame Eder Bonfim header to squirm through his grasp and over the goalline to earn Steaua Bucharest a 1-1 draw in Romania.
However, the 3-3 draw between FC Utrecht and Napoli meant Liverpool did enough to win through as Group K leaders with a game to spare.
But Reina, who was captain for the evening in the absence of injured duo Steven Gerrard and Jamie Carragher, accepted the result could have been better but for his mistake.
An experimental Liverpool team packed with fringe players and youngsters had taken the lead through Milan Jovanovic's 19th-minute header.
Liverpool manager Roy Hodgson chose not to dwell on Reina's error, and instead pointed to an encouraging performance from his much-changed team.
Cole made his comeback after more than a month out through injury, while Ryan Babel, Milan Jovanovic and Fabio Aurelio were all handed rare starts in a team that also included youngsters Martin Kelly, Dani Pacheco and Danny Wilson.
And Hodgson believes his policy of giving the whole squad an opportunity in the Europa League is paying dividends.
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The 32-year-old suffered the injury in Sunday's Premier League defeat at Tottenham. 
The 30 year-old has been ruled out for a month, which could have a significant effect on his side's season after a recent revival came to an end at Stoke last Saturday. 
