Manager Rafael Benitez admitted they had only themselves to blame after suffering an agonising Champions League exit.
After beating Debrecen 1-0 in the Ferenc Puskas Stadium, the Liverpool players watched anxiously on a television monitor in the tunnel as their fate was sealed.
Night of pain: Liverpool coach Rafa Benitez looks on as Steven Gerrard walks off the field
Fiorentina hung on to a 1-0 win of their own at home against Lyon, who they join in the first knock-out round.
There were no excuses from the Spanish manager, a Champions League winner in 2005 and runner-up in 2007, as he pinpointed last minute goals in both games against French side Lyon as the moments that cost five-time European champions Liverpool qualification from the group stage for the first time in seven years.
Blow: Steven Gerrard couldn't hide his disappointment as Liverpool were knocked out of the Champions League
'We did our job tonight, and I couldn't have asked for any more, butif you look back over the group, those two late goals made a massivedifference,' he said.
'We made mistakes in those games in the last minute, so we have to accept it's our fault in the end.
'I'mreally disappointed because we had so many chances in every game andcould have won them all. 'This really hurts, especially the way we areout. You think back to those two goals against Lyon and realise thatavoiding just one of them could have made all the difference. We couldstill have been in there fighting. But we can't change it now and haveto be positive.
'We have to make sure we are at our best in our next game againstEverton because the target now has to be to try and put a winning runtogether in the Premier League.'
Benitez insisted Liverpoolhad become a victim of their own success in the Champions League afterqualifying for the knock-out phase every season since he took over in2004.
'We are in a very bad position and can't win the Champions League now,' he said. 'But it is worth remembering a lot of teams don't even make it into this competition. Because we have qualified for five years in row, people think it's easy, but it's not.
'I don't think the disappointment will linger with theplayers. They know it has been a bad run of games and that they couldhave been better in at least two of them. But at least they won tonightand showed a lot of character, and they deserve some credit for that.
Bitter pill to swallow: David Ngog scored Liverpool's goal against Debrecen but the Merseysiders have still been knocked out of the Champions League
'Ifeel so sorry for the players, staff and fans, but we will pickourselves up and be in the right frame of mind for the derby. Ihonestly think people have got a bit complacent about us in thiscompetition because we go through every year. They are expecting us toget to the final every year, but no-one has a divine right to do that.
'Weknew at half-time Fiorentina were winning, then at the end, we werewaiting for the final whistle over there. It was difficult to take, butall we can think about now is winning the derby on Sunday.'
Captain Steven Gerrard was crestfallen but insisted his club should now concentrate on winning the Europa League, having won the UEFA Cup just eight years ago.
'Of course it's disappointing, we played fantastically well tonight and despite getting three points we don't progress.
'Hopefully now we'll be in the Europa League so we'll try to win that.
'The main prize has gone and to be playing in the Europa League is disappointing but we have to accept that, move on and try to win that competition.
'The only consolation in this is if we go on and win the secondary one.'
Horror show: Liverpool's anguished players watch on a TV in the tunnel area as Lyon miss a late chance against Fiorentina to seal their fate in this season's Champions League
Arsenal boss Arsene Wenger, whose side sealed their passage to the last 16 with a 2-0 win over Standard Liege at the Emirates thanks to goals from Samir Nasri and Denilson, insisted he was not surprised Liverpool were eliminated from the competition.
Wenger said: 'You always favoured Fiorentina at home against Lyon, who are not on an especially good run, to qualify for the first time in their history.
'I thought it would be difficult for Liverpool to qualify.
'They can, of course, respond well and do well in the Europa League.'
When asked if Wenger was glad his Premier League rivals were out, the Frenchman replied: 'Frankly, no. Anyway, If Liverpool are out, another big team is in. We cannot play against them in the next stage anyway.'
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