The Reds suffered a narrow 1-0 defeat at Estadio Metropolitano on Tuesday night in the first leg of their Champions League last-16 tie with the La Liga outfit.
The visit of West Ham United to Anfield on Monday night in the Premier League is next up on the schedule, with Klopp viewing the fixture as an opportunity for his side to get quickly back on track.
"It's to put things right, just not in the [same] competition," the boss said at his pre-match press conference. "It's a little bit strange, yes we lost the game and there's absolutely no positive in it, we lost the game. But it's important if there's any help in that result it's that you felt that defeat and it felt like a defeat.
"It felt after the game like a defeat, it felt the next morning like a defeat, it was nothing. Nobody thought, 'But in the league we are like this'. It's all what we said after the game, like it's not done yet – it's the truth, we know that.
"But it's not that we say that Anfield alone will sort it at the end. We have to put a proper performance in. Atletico showed obviously a lot of passion, desire and stuff like this, fought for the result. They will fight here for the result, 100 per cent.
"But to put it right is to get the other feeling back. The other feeling, I don't think we ever lost how a win feels, but we won a few games, so now we lost it and the difference is massive – much more than three points.
"It's really from sunshine to hardest rain – and that's how it should be. If you really want to be successful and if you could be successful – what we could have been in that game – then it has to feel really bad and that's how it felt.
"So yes, we want to put things right, even when it's a different competition."
West Ham currently lie in the relegation zone and met Liverpool last month at the London Stadium as the Premier League leaders recorded a 2-0 victory thanks to goals from Mohamed Salah and Alex Oxlade-Chamberlain.
But the performance of David Moyes' team at Manchester City on Wednesday evening reinforced Klopp's view about the threat they pose to the Reds.
"With all the brilliance which we know about Man City, the first goal was a set-piece," Klopp continued. "And the second goal was a super situation from Kevin De Bruyne obviously.
"But, at the end, it was a little bit scrappy with Bernardo Silva and he takes the ball over and it's kind of a one-two in the box. Super goal, but not outplayed like you would expect when City is on the pitch.
"They fought really hard, they defended the box with all they had. They didn't have a lot of possession obviously, so I wouldn't expect that they go for much more possession against us. But they will defend again with all they have.
"I didn't hear exactly what David said after the game, but I think they took some positives out of that game and they will try it again. We have to be ready for that.
"It's Monday night, we need a really good atmosphere again and not kind of this perception that you go there and think, 'OK, 1-0 after seven minutes, 2-0 after 25 and then it's easy-going'. It will not be like this.
"West Ham needs to fight for results and they will fight for results. They have tough games coming up for them as well, so they don't have time to waste results, points or whatever. I expect a really, really tough match, 100 per cent."