West Ham boss David Moyes accepts Everton deserved their win on Sunday.
Dominic Calvert-Lewin struck for the 1-0 triumph in London.
Moyes later said: "They were always going to give you the ball and we'd have more of it, and I think we did, but ultimately you have to score the goals.
"We've had games here recently when we haven't had much of the ball but we've scored the goals on the counter-attack. I'm not saying that was their goal today but it was a little bit like that.
"We were the ones who got done by a counter-attack, really.
"I think we were probably the better team and I thought we looked the more likely to score in the second half as it went on and we looked a bigger threat.
"In the first half I thought we did quite well with the ball but we didn't really go anywhere with it.
"Everton are really good at what they do.
"If you look at how hard their wide players and full-backs work to stop crosses coming in and forcing us to go back and play inside regularly. That was a feature and we were aware of it.
"This was a game I was worried about in many ways as Everton have been much better away from home and they're a side who it took Liverpool 65 or 70 minutes to get the first goal against last week, so they're not a side who are giving up goals easily."