Klopp says the Saints 'are really just difficult to play' against.
Jürgen Klopp saluted Liverpool's 2-1 win over Southampton on Saturday.
Sadio Mane followed up his brace in Istanbul during midweek with another impressive display at the St Mary's Stadium.
The Senegal international scored the first goal of the game to put the Reds ahead at the stroke of half-time. And, that was before Mane assisted Roberto Firmino to double the lead in the 71st minute.
However, former Reds striker Danny Ings scored a consolation goal late on for the Saints as he took advantage of Adrian's error.
Following the game, Klopp was asked whether the win was ‘bigger than it might have been’ given his side’s UEFA Super Cup exploits in midweek, and he replied as the club's official website reported: "No. We played here last year I don’t know after which game and it was difficult. Southampton is a good team, they defend well, they are really just difficult to play.
"Good counter-attacks, good organisation, all that stuff. Last year, we were 1-0 down and won 3-1 right? That was really difficult and this afternoon it was difficult again.
"Nothing to do with the game in midweek: I said before the game, if we would have come here with two weeks’ preparation it would be difficult.
"So I liked the game a lot, to be honest. It’s not allowed to think too much about Wednesday but of course I know it, so I was really impressed with how fresh we looked, in the start especially, just how good we were."
The German continued: "We controlled the game, we were fluent, all that stuff and then with the long balls and set-pieces Southampton came up then. But Sadio scored a fantastic goal in pretty much the best moment at least of the first half, in the last second pretty much. That helped, of course, and in the second half we made other big steps.
"We really controlled the game better, did a lot of good things, and then minute 83, I saw it up on the screen, and Adrian thought ‘I played really well, so maybe I have to make the same mistake as Ali did!’ and kept the game a little bit open. So then they came up and Ingsy had a big chance.
"That’s normal and I think then the boys felt the tiredness, that was the moment you think, ‘Really? Now we have to go again?’ So, we kept the result, I think we deserved the three points and I’m completely fine with that."
When asked if he spoke to Adrian about his error, Klopp said: "Yes: ‘You finally arrived, welcome!’ Ali did the same. Obviously it’s a goalie thing at Liverpool, no problem with that as long as we win the games. All good."