Diogo Jota and Cody Gakpo both struck twice, with Mohamed Salah also scoring. West Hamhad gone ahead through a Jarell Quansah own goal.
Lopetegui later said, "I think it was an even game for 60 minutes.
"I think we played one of our better matches, but you can’t say that when you look at the scoreline. We didn’t deserve to lose by this scoreline, as we had a lot of chances. We suffered one goal, which was offside in the first half, and that’s the reason why I love VAR.
"In the second half we could have had a penalty, and the next action they score the second goal. After this, we did very, very well and were still in the match until 70 minutes.
"We had many clear chances to level the match but didn’t score. When we went down to ten players, it became a lot more difficult, but sometimes this can happen.
"I think we had very good actions and showed more personality, character, and more of what we want to do with the ball.
"There are positives, though, such as the players who played for the first time in the starting line-up, though it is not easy to say that today.
"Today was a hard day, because first of all we had a big expectation in this competition despite playing at Anfield against Liverpool.
"We are now eliminated from the Carabao Cup, and now we have to put our focus on the more important competitions, such as the Premier League.
"I think that we have to think about the next match against Brentford, as this is a very important match for us. We have to be ready to compete and take the positives because they are going to demand this."