Kenny Dalglish said his side lacked fortune and creativity as defeat to Braga left them facing the prospect of a season without European football.
The Reds struggled to break Braga down as the visitors held onto their one-goal advantage given to them by Alan's penalty in Portugal a week ago.
Even a first start for £35 million club record signing Andy Carroll could not help find a way through as Liverpool's hopes of qualifying for Europe next season were dented.
"Over the two legs, a penalty has separated the two teams," Dalglish said. "There wasn't much between either side.
"They were very well organised and we knew the responsibility was on us to break them down and score a goal. If Andy's header had gone in in the first half it could have been a different outcome, but we never put anything past the goalkeeper.
"You need to be really strong creatively if you are going to break down a very organised side or you need a bit of luck and we certainly have not had much fortune over two legs - but I guess everyone says they should have more luck then they get.
"Like every other team in the world we could do with a bit more creativity but we are no different than anyone else."
Liverpool will now have to finish fifth or higher in the Premier League if they are to participate in European football next season, but their defeat to Braga does mean they will not have any distractions from other competitions.
"I don't know if it will be a help not being in the Europa League," he said. "It was an option for us to get back into Europe next year if we'd won it.
"We know that in every league game we will have to try and get as much as we possibly can. We were going to do that anyway, so I don't know if it will be a blessing or not. You only get in Europe if you win games. If you win enough games and get enough points we will get in Europe."
Dalglish was pleased with the performance of Carroll, after two substitute appearances, even if the striker could not make the breakthrough.
"Carroll stayed on longer than we hoped he would have to stay on but necessity meant he had to stay on the pitch because we were looking for a goal," he added.
"Overall we are pleased to see him back on the pitch and we were not disappointed with his contribution in any way. It was a bit unfortunate he did not score a goal; he put one header wide in the first half and then had one stopped by Dirk Kuyt in the second.
"Considering it was his first start I think he can be very pleased with how he played."
Braga coach Domingos Paciencia made no apologies for the way his players celebrated at the final whistle after the club reached the quarter-finals for the first time in their history.
"We have reasons to be proud tonight," he said. "We achieved a different level that we have never achieved before.
"I ask Liverpool supporters to appreciate the way we celebrated the way we did because this is a different level. Don't take things the wrong way for the way we celebrated. We are proud."