Mane’s brace and van Dijk’s towering header helped the Reds reach the last eight of Europe’s elite competition for the second successive season and Klopp said Liverpool deserved the triumph.
Jurgen Klopp heaped praise on his side after they beat Bayern Munich 3-1 at the Allianz Arena to book a spot in the Champions League quarter-finals.
The Merseyside club broke the deadlock at the Allianz Arena through Sadio Mane but an own-goal from Joel Matip levelled for the Bundesliga champions before Virgil van Dijk handed the Reds the lead again with a powerful header and Mane scored his second on the night to seal the win.
"In a game like this you can never rest. It is absolutely deserved. It is so difficult to play here away at Bayern Munich,” Klopp told BT Sport.
"It is a big one. I am so proud of the boys. Jordan Henderson twisted his ankle. Hopefully it is not too serious. Making early changes is never a good time.
"The first goal, I will want to watch it back like 1,000 times! Defensively it was so good. We didn't defend the way we do usually in the away games of the Champions League but today we did.
"Virgil van Dijk gives organisation on set-pieces and he is dangerous. He is a massive threat. The size we have and the power we have... it was a big goal.
"In a game like this, there will be mistakes but you have to stay in the game. Control the moments you can control and stay in the game. The game didn't look like Bayern ever outplayed us.
"We scored the other two and could have scored another one with that chance for Mohamed Salah."