Despite Liverpool beating Debrecen 1-0 in Hungary, a victory for Fiorentina against Lyon consigned the 2005 champions to the Europa League.
"It was our own fault in the end, the late goals we have conceded along the way have cost us," said Benitez.
- Debrecen 0-1 Liverpool
- Champions League fixtures
"We had to win our game, we couldn't control the other game.
"I think because we qualified the last five years, everybody was expecting it would always be the same - but sometimes in football, these things can happen.
"It's really disappointing because we conceded two late goals and we are paying for this. But if you analyse all the games, yes, the first half against Fiorentina we didn't play at the required level, but afterwards we could have beaten Lyon and we could have scored against Fiorentina too.
"I was talking with two or three senior players and they realise that to achieve the knockout stages every year is not easy. So they know that we have to change our target, to think about the league, the Europa League and the FA Cup. We want to finish as high as possible.
"The players are a little bit down, but they also know that we could only win our game and wait."
- Football.co.uk staff