Tigers substitute David Meyler pulled one back shortly after the break but Philippe Coutinho immediately restored the three-goal cushion before Milner added his second from the spot when Daniel Sturridge was fouled.
"The first half was brilliant, that was how football should be if you are able to do it," Klopp said.
"In the first few minutes you could really see how strong we could be in counter-attacks.
"I was a little bit surprised of the speed and power of these situations.
"The most impressive thing today was the counter-pressing: I think it was the best game we played in counter-pressing until now.
"Second half was not as exciting, still good but not at 100 per cent of concentration.
"I don't want to criticise but I think we could have done better in the second half.
"It was good, but not as good as it could have been.
"We have a lot of things to improve and one is that if you are brilliant you need to be brilliant for 95 minutes."