Klopp's men had little difficulty cruising past Southampton, with Roberto Firmino opening the scoring early on to set the Reds on their way after Mohamed Salah had pounced on a Wesley Hoedt error.
Firmino then turned provider just before the break, returning the favour to Salah, who finished with aplomb to effectively end the chances of a home side who got progressively worse after the break.
"We knew the strengths of Southampton and how they want to play football, so we wanted to defend and change the game to counter," Klopp told Sky Sports.
"In footballing moments we would've loved to do it [play] a bit better. The rhythm wasn't good either, too fast or really slow and not normal passing speed.
"We scored wonderful goals and we could've scored more in the second half when we had big chances, but Southampton did well to be honest, with their style of play.
"That's how they want to solve their situation and their problems. I think we deserved the three points, [we got a] clean sheet, no injuries – [it was] nearly perfect."
The match saw Virgil van Dijk make his first return to St Mary's and he received a hostile reception, with Saints fans jeering him whenever he touched the ball.
But it did not appear to get under his skin, as the Netherlands international just did his "thing".
"I enjoyed it a lot," Van Dijk said. "I just focused on the game and I enjoyed being back here because I've a lot of good memories here.
"Unfortunately they're not in a good position right now, but as a Liverpool player I am happy with the win. You can't do anything about the reception. I just did my thing."