The Reds came from 2-1 down to win 3-2 to maintain their unbeaten record in the Premier League.
Klopp told Sky Sports: "I liked a lot how we started. We scored a wonderful first goal. But then we weren't good in second ball situations. We have to pick them up much more often. We struggled in this situation and that gave West Ham a good feeling.
"They could win the second ball from the goal-kicks and for us that was difficult. We lost a little bit of patience in the first half in the things we did. Offensively, you could see this a little bit.
"They scored the second goal and I have to watch back how that happened. Then we were forced to stay calm and do the right stuff.
"All the goals we scored were strange. The best goal we scored didn't count because Sadio [Mane] was offside. You have to squeeze it and that's what we did tonight to get the three points and it is so special."