The champion of English football's first and second tiers were paired together to launch their campaigns and Mohamed Salah's fourth-minute penalty suggested Liverpool could be on course for a straightforward win.
But Marcelo Bielsa's Leeds equalised three times over the course of a compelling contest before Salah broke its heart with a second penalty to complete his hat-trick and snatch a 4-3 victory two minutes from time.
Reds boss Klopp was keen not to dwell for too long upon his own team's unusually slack defending.
"What a game, what an opponent, what a performance from both teams. A proper spectacle, I loved that," he said.
"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 [to improve].
"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 pre-season and it takes time to all come together again. I am really positive about this game."
Leeds is playing in the top flight for the first time since 2004 and Klopp feels it will be a success if it can maintain the levels it showed on Merseyside.
"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?" he added.