Kudus made his first start in the competition at London Stadium, but could not find a way through as the Hammers fell to a 1-0 loss against Sean Dyche’s hard-working side.
Dominic Calvert-Lewin claimed the only goal in a game of few clear chances early in the second half to condemn David Moyes’ men to a third successive defeat, after losing at Aston Villa and, in the Europa League, against Olympiacos.
But the 23-year-old Ghanaian, who also started against the Greeks, is backing them to bounce back in the Carabao Cup against Arsenal.
“It was very disappointing,” Kudus told West Ham TV.
“We want to win every game, but it’s done now and we need to focus on the next game.
“We definitely want to bounce back against Arsenal. The good thing is there are a lot of games and we don’t have time to be too disappointed.
“The focus now has to be on Arsenal, our next game, and how we do better.”
England goalkeeper Jordan Pickford had to make a key save from Hammers substitute Said Benrahma in injury time, but was not seriously tested other than that.
The hosts had nearly 65 per cent possession but could not break down a dogged Everton rearguard.
Jarrod Bowen fired wide and headed over, either side of the break, and Kudus added: “From the start of the game, we knew we were playing against a very compact team.
“We knew we would have to do more to create a lot of chances, but we didn’t manage to do that.
“If you don’t score then you need to not concede, but we didn’t do that today. We need to learn from that.”
Kudus started on the right flank, in his first Premier League start since joining from Ajax for £38million in the summer, and was grateful for the chance to show his abilities.
“I know what I can do,” he said, after making his 11th appearance in claret and blue.
“I believe a lot in myself so I’m just here, trying to settle in and take in as much information as I can.
“I want to input that into my game and do what I can for the team.
“The expectation in myself is there. Everyone expects from me because I know myself better than anybody else.
“I think my best position is as the number 10, as the attacking midfielder, but as a team player, when I find myself on the right side then I just want to do my best for the team.”
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