The defeat was the heaviest by any English side in their Champions League opener since Arsenal lost 3-0 to Inter Milan in 2003.
Liverpool started the game on the wrong foot and were 3-0 down before the halftime whistle.
Piotr Zielinski, Frank Zambo-Anguissa and Giovanni Simeone scored for the hosts in the first half while Victor Osimhen had a penalty saved by Alisson Becker.
Zielinski added a fourth shortly after recess before Luis Diaz scored what proved to be a mere consolation.
After so much success in recent years, opponents have worked out a way to nullify Liverpool's threat and Klopp is keen to find another way to get back to top form.
"Really tough to take, it's not that difficult to explain when you watched the game. To start with the two penalties, okay first of all Napoli played a really good game, we didn't, that is the first explanation for the defeat," the German told BT Sport.
"They scored one penalty and missed another but the next two goals we served on a plate, that's not cool and we should defend better. Then 3-0 down having chances but never really in the game.
"We were not compact defensively or offensively. Until Thiago [Alcantara] entered the pitch I cannot remember one counter-pressing situation, we were too wide.
"Everything is obvious but why it happened is now the question, I cannot answer now, let me think about it. It is a really tough cookie to take, but I have to take it.
"We played bad first halves, unfortunately, usually we don't concede three, though – with Alisson in the goal you have to be really bad to do it. We did the same here when we lost 2-0 [in 2019-20].
"It looks like we have to reinvent ourselves, there's a lot of things lacking – not in all games – but the fun part is we have do that in the middle of a Premier League season and Champions League campaign."
