Promoted Leeds, back in the top flight after 16 years, fought back from a goal down on three occasions but Liverpool emerged with the three points after an 88th minute penalty from hat-trick hero Mohamed Salah.
"What a game, what an opponent, what a performance from both teams. A proper spectacle, I loved that," Klopp said after the match as his team extended their home unbeaten streak in the league to 60 games.
"It is pretty rare you see that many goals in a game, we have left space for improvement in our defending but that is not unusual for a first game. Our players have played a few days ago for their countries so it is possible."
Klopp added that the defensive errors were not just down to rust, with Marcelo Bielsa's Leeds -- who won the second-tier English Championship title in 2019-20 to earn promotion -- causing them to make errors.
Klopp said: "The opponent forced us to make mistakes. We can do better, we will do better, but I loved a lot about the game against a well-organised, passionate side like Leeds. We used our skills to cause them problems, we could have scored more and in the end we used set pieces, which is fine by me.
"It is not like riding a bike, you can lose something in preseason and it takes time to all come together again. I am really positive about this game. Leeds will have a good season if they can keep up that intensity and they did it in the Championship with more games so why not?"
Information from Reuters was used in this story.