"He's in a very good moment. Whether he's the best (English striker) I don't know, but I don't care. For me, for us, he is."

Victory may have come at a cost however, as Richarlison hobbled off shortly after firing Everton back in front in the 56th minute, while there were also problems for Allan and Jonjoe Kenny.

Ancelotti played down those injuries, but admitted Allan and Kenny may now miss Saturday's game against Brighton.

"Richarlison has a twist on his ankle but I think it's not so bad," Ancelotti said. "Allan had a muscle problem and Kenny a twist on his ankle. We have to check them tomorrow but it seems no so bad...

"Richarlison I think can recover for Saturday, Allan and Kenny will be more difficult."

The win extended Everton's perfect start to the season to six games in all competitions, and they will be taken seriously in Thursday's quarter-final draw as they seek their first silverware since 1995.

Ancelotti continued: "We have started really well. It was not a surprise because I think that his squad has a lot of quality.

"We were able to adapt very well with the new signings but the others came back with different ambitions and different motivations so now we are doing well."

Everton were able to cut through West Ham repeatedly as a strong line-up that included James Rodriguez as well as Richarlison and Calvert-Lewin caused the Hammers all manner of problems.

But the visitors did not help themselves with lax defending clinically punished.

Snodgrass gave them hope when he levelled just 25 seconds into the second half, but it was about the only thing that went right after the break and Everton killed them off after Sebastien Haller's acrobatic overhead kick went straight at Jordan Pickford.

"In the second half obviously we got off to a great start but then we conceded three really poor goals, all preventable, all things we'd like to think we wouldn't do," said assistant manager Alan Irvine.

"I don't think the result was a fair reflection of the game overall. We had a big moment at 2-1 down when Haller had a fantastic overhead saved, either side of Jordan it goes in but that was one big moment and the next big moment was conceding the third goal."

Irvine was again filling in as David Moyes self-isolates following a positive test for coronavirus, and the Scot said the Hammers need their manager back as soon as possible.

"We have a replacement for every player in every position but nobody has a replacement for a manager," he said.

"The players get proper answers from a manager and I'm not able to answer a lot of things players are asking because I don't have that role and that responsibility. We need David back soon."

Everton have been linked with a move for Norwich defender Ben Godfrey, but Ancelotti had little to say on the matter after the match.

"I have said in the past we are looking for a centre-back because we are short there," he said. "Godfrey is a really good centre-back but he is playing for Norwich and I cannot say anything more."