The Reds came into the match on the back of a narrow 1-0 loss to Premier League rivals Chelsea via a 10th-minute Gary Cahill goal, but second-half strikes from Divock Origi and Roberto Firmino ensured Klopp's side claimed a well-deserved victory against the Italians.
Speaking after the match, the German tactician said: "In the first half we played brilliantly, we did the right thing - passed and passed and passed all the time until we were through."
Klopp admitted that there was still plenty of work to be done, though, before the team reaches its true potential.
"We created chances and didn't score, we didn't finish. But it will come, 100 per cent. Again we lost a little bit of patience and chose the wrong way because we had one or two long balls too many and forced the play when we lost the patience to pass again. So we created our problems, but it was not the biggest problem. There are a lot of things to do."
The former Borussia Dortmund boss also had words of praise for Milan, who drew 3-3 with Carlo Ancelotti's Bayern Munich in their previous ICC clash.
"Italian teams are always well organised and always make problems. You always struggle with different things in the game because it’s not easy to play them," he added.
"We did really well and scored wonderful goals. We had one or two more chances and especially in the first half we had four or five big moments.
"We were playing dominant football and then reacting on balls we lost, like we did in counter-pressing situations. That’s the only moment where it should be a little bit hectic.
"All the rest should be calm and really dominant. I'm pleased with the performance of the whole team."