The Reds broke a run of three straight losses with a convincing win at the Puskas Arena in Budapest.
Liverpool have not been at their brilliant best in recent weeks and Klopp says many people were waiting for the Premier League champions to falter against Die Roten Bullen.
After a tepid first half which lacked invention and imagination from both sides, Mohamed Salah broke the deadlock following a terrible defending from the Germans seven minutes into the second half.
Sadio Mane doubled the English side’s advantage five minutes later after another blemish at the back.
"It was the game we wanted, the game we needed. RB Leipzig can be a real monster, they overrun teams, they are really physical and we controlled them in an exceptional way. We played a really good game and we got the result we deserved,” Klopp said after the game.
"We defended really well and had good recovery. It was a tough game with only two days since the last one. It's only the first leg, we know that but a lot of people were waiting for us to slip again.
"For two years we were really good and this year we have problems, that's fine. A lot of people expected us to slip again but the boys didn't."
Liverpool will hope to translate their big win in Europe to the Premier League when they entertain local rivals Everton in the Merseyside Derby on Saturday.
