Liverpool tried desperately last night to put a brave face on their first Champions League exit at the group stages for six years.
Chief executive Christian Purslow insisted manager Rafael Benitez's position "is under no threat" and skipper Steven Gerrard vowed that Liverpool would win the Europa League.
Benitez, meanwhile, claimed he was "more disappointed for the players, the staff and the fans" than for himself.
But in the cold light of day they will no doubt review the 1-0 win over a poor Debrecen side - with Fiorentina securing qualification by beating Lyon by the same scoreline - as a bitter pill to swallow.
Purslow made a point of doing media briefings after the game, and said: "You can never predict last-minute goals, which have cost us dear in the Champions League. That's no basis to make managerial decisions.
"We don't run our business in that respect. I'm on the record as saying Rafa's signed a new five-year contract, he's four months into that contract so to discuss that is not appropriate. He is under no threat."
Referring to the financial damage of missing out on qualification from the group phase, Purslow added: "It's limited actually. Assuming we have a reasonable run in the Europa League then we are financially neutral for this year."
After David Ngog's early strike had secured Liverpool their win in the Ferenc Puskas stadium, Gerrard said: "Of course it's disappointing, we played fantastically well tonight and despite getting three points we don't progress.
"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 for us now is if we go on and win the secondary one."
Benitez turned the focus onto Sunday's Merseyside derby at Everton, and said: "It was our own fault in the end, the late goals we have conceded along the way have cost us. We have been so good in the last few years that maybe people think it is easy to qualify in all competitions.
"Because of that, people think we can do it every season. But you cannot always, now we have a massive game on Sunday at Everton and we have to be ready for it.
"We have to be disappointed, we knew we had to win and we did that. You cannot change what happened in Florence, but at least we did our job.
"If you analyse the other group games, losing two late goals in two games with Lyon has been the massive difference. It has cost us four points from goals conceded in injury time.
"I like to win every game, I like to be as high as possible in every league table. But I have to be positive because you could see the players working so hard on a very difficult pitch.
"In this situation I think more about the players, the staff and the fans. I am disappointed for everyone.
"Now we have new targets. We are in a very bad position because now we cannot win the Champions League again, we know that, so the next game has to be won."