When Moyes named the starting 11 ahead of kick-off, it was made clear that Grealish, who missed Saturday’s 2-0 loss to Arsenal through illness, was this time absent for disciplinary reasons after what the Press Association understands was an unauthorised absence from training.

Moyes refused to give further details, saying only: “It was a club decision. I support the decision. It’s something I don’t really want to speak too much about.”

But when asked about the response of his players on a night when the matter could have been a distraction, Moyes said: “I think the one thing about Everton and what they’ve got is they’ve got really good values behind it.

“All the players stand up to the values, accept the values that we put out there, what we want from them on the pitch and off the pitch.

“And from that point of view I think the players have done a brilliant job tonight, they really did.”

Everton took control of the game in the first half with goals from James Garner and Hayden Hackney before Thierno Barry ended any doubt in the 69th minute, with Dan Burn scoring a late consolation goal.

Victory sets up a quarter-final against Fleetwood after the League Two team stunned Premier League champions Arsenal on Tuesday, giving Everton a clear path to the last four of a competition they have never won in their proud history.

“I think the minute you use the word quarter-finals then you start to think, ‘this sounds good’,” Moyes said. “I think we’re pleased that we’ve been able to get to this stage of the competition. If we can keep it going great, obviously.”

Newcastle boss Matthias Jaissle made clear his frustration as any good feeling left from Sunday’s 2-0 win at Crystal Palace evaporated.

“We of course are disappointed with the result, it’s also a bit shocking at the moment because overall the game was not that bad,” he said.

“But it’s a bit the story of the season so far, that in situations where it really counts we lack the clinical approach to solve the situations.”

Everton took the lead when Amar Dedic was harried into a poor clearance by Tyrique George, losing the ball before Garner swept home, while the second goal came moments after Newcastle’s penalty appeals were rejected by Farai Hallam after Harvey Barnes went down in the box.

“Just thinking about the first one again, it’s no risk zone, we (should) clear the ball and nothing happens, and a couple of seconds later we concede a goal out of nothing,” Jaissle added.

“The second one is also frustrating in my point of view, we deserved to have a penalty, on the other hand then we miss in a transition to defend our own box which again is difficult to accept. We have clear rules then how to behave…we need to learn quickly…

“For me it’s about being mature in the situations, more clinical to solve the situations and not allowing almost a gift for the opposition to score.

“It feels like the opposition is not giving us these gifts at the moment so we need to avoid that.”