A goalless draw at home to Real Madrid, after squandering a number of chances, meant the 3-1 quarter-final first-leg defeat last week ended their interest in the competition.
The six-time winners remain outside bets to secure a top-four Premier League spot, which would qualify them for a fifth successive campaign, but they will have to get past at least West Ham (three points ahead) and Chelsea (two), although the faltering form of third-placed Leicester (four ahead) may open up a second spot.
“I would say I am naturally confident, but that doesn’t mean we will end up there,” said Klopp on their top-four hopes.
“We just can read the table, we know the points, we know the situation and stuff like this.
“We know who we play and we don’t have to talk too much about it. I said now what we think about it and, yes, we want and we have to – and if we want that we should play really good football.
“So we just have to keep going. We really have to keep going, we have to keep fighting.
“We want to be in the Champions League next year but in the moment we still have to pick up more points than a lot of other teams.”
But there were other culpable players as 15 attempts registered just four shots on target.
It is a failing they cannot allow to continue if they want to fulfil their ambition but Klopp said the performance offered some encouragement.
“That will not happen that it impacts us negatively. We are not silly. We want what we earn,” he added.
“If we don’t earn it 100 percent, then we respect the situation that we don’t get it.
“But it has now no impact on the Premier League, apart from that we don’t play midweeks at least internationally – I’m pretty sure Premier League plays midweeks – so we can concentrate and focus on the Premier League.
“But it’s tough just because we are still not in the hot seat, I would say, and we face Leeds on Monday, so that’s a tough one.
“They are the leader in all physical stats in the Premier League pretty much, so you better run a lot yourself.
“We have a few days until then, we will use that and then we make sure we are ready for that.”
Thursday is the 32nd anniversary of the Hillsborough disaster, where 96 fans lost their lives at an FA Cup semi-final against Nottingham Forest in Sheffield.
The club will mark the occasion privately with players and staff observing a minute’s silence, with floral wreaths laid at the Hillsborough memorial at Anfield.
Flags will be flown at half-mast and the Anfield retail store will close from 1pm for the remainder of the day.