The Reds were beaten 5-4 on spot-kicks at Munich's Allianz Arena after the game had finished 1-1, with Roberto Firmino converting from 12 yards to cancel out Keidi Bare's first-half opener.
The contest brought to an end a week-long stay in Germany for the club and Klopp is pleased with how his side benefited from the training base in Rottach-Egern and three friendly matches in his homeland.
Read on for a summary of the manager's post-match press conference.
On his general overall view of the game…
If you get to a penalty shootout you want to win it, but that's not the important situation that we have today. The boys played really well, they were very good in their preparations and you couldn't have had a more difficult job than we did today against a team like Atletico, who get results, results, results. We had a lot of substitutions and were a bit tired from all the training, so it can't be easy. If you can do it better then great. In the first half, we had a few nice moments where we had some good crosses. It was really tight, but when we conceded we didn't think straight away and the formation wasn't 100 per cent. One lost challenge with a header shouldn't mean you go behind. In the second half, we played much better but the situation continued to be very difficult. We lost the penalty shootout, but I am not absolutely down and out about it.
LFCTV GO: Atletico clash in 90 seconds
On what he takes from the training camp in Germany…
We've really trained hard, the boys have been great about it and done everything I've expected from them. We've had a very intensive programme, so that's why I am very, very happy with it. We didn't have freshness today, but we still have one-and-a-half weeks until our first game [at Watford]. That's the time we need to prepare for it. I am satisfied with how it is. It's very easy – next season we want to be as good as we can possibly be. We want to be better than last year, which isn't easy, but we don't set any limits to ourselves.
On the upcoming Champions League play-off…
These games are always very important and you're playing at the top level, so it's very important how you prepare and what kind of state of mind you're in. If you want to win, obviously you want to [draw] a smaller opponent, but we played against Bayern yesterday and we can play much better.
On fatigue after two Audi Cup games in two days...
We're very tired today and we want to make life as difficult as possible for our opponents. The only [bad] thing that happened here today was the goal we conceded. We had 20 shots on goal, and you've got to do something from that, but Atletico are a very strong team. For many players, this is a real experience. It's a [difficult] situation that you [ask] the players to play a game they shouldn't be playing. Many things were really good about this, everything went really well and with one or two players things didn't work out too well. But I'm really happy we still have one-and-a-half weeks and I'm happy that we don't have to play tomorrow!
On Joe Gomez at centre-half...
How you know, Joe can play both positions [centre-back and right-back] so it makes absolute sense that we try both positions, especially in our situation with [Nathaniel] Clyne injured. He's on the way back but he's had no pre-season so far so, for him, it will not only be tight for Watford, it's pretty much impossible. So we have, in the moment, three options for this position: Trent Alexander-Arnold, Joe and Jon Flanagan. All of them played the position and now we have to bring them through the next one-and-a-half weeks and hopefully Clyney can come back after this. We have to make a decision. For Joe, after the long injury he came back in the middle of the season and was not as quick as he was before. But he got it all back and he's in really good shape and so it's very important for us that we could bring him in both positions.