Mane was substituted at half-time of the 1-0 loss after he was booked for catching Sime Vrsaljko in the face with a stray arm.
Klopp said: "It was not exactly what should happen but it happened. It was the fight we expected and the atmosphere we expected but I love so many parts of our game. It is only 1-0 down at half time and the second half we play out our stadium.
"We lacked in the final third. They defended with all they had - their defending in the box was incredible. When you are 1-0 down with a team like this who only want this kind of result - 0-0 would have been good for them.
"He [Sadio Mane] was targeted. It was clear. They wanted to make sure he got a yellow card. It is only half time but you need to be really strong as a referee in this atmosphere. Already in the first 30 minutes three of their players went to the ground I don't know what for. Nobody to blame. I am fine, 1-0 down at half time we have the longest half time break and we will use that."