David Moyes pointedly praised Everton's "really good values" after Jack Grealish was dropped for breaching club discipline prior to Thursday's 3-1 win over Newcastle in the League Cup.
Grealish reportedly skipped training ahead of the fourth round tie and was left out of the Everton squad at the Hill Dickinson Stadium.
The on-loan Manchester City winger had missed Everton's defeat at Arsenal in the Premier League on Saturday due to illness.
Everton boss Moyes refused to give further details on Grealish's absence against Newcastle, but backed the move to leave him out.
"It was a club decision. I support the decision. It's something I don't really want to speak too much about," he said.
Asked about the response of his players on a night when the controversy could have been a distraction, Moyes's answer suggested frustration with Grealish, who has repeatedly been criticised for his off-field behaviour.
England international Grealish fell out of favour at City after several late-night incidents and reports of after-hours drinking.
"I think the one thing about Everton and what they've got is they've got really good values behind it," Moyes said.
"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.
Dan Burn scored a late goal for Newcastle but Everton eased through to face fourth-tier minnows Fleetwood in the quarterfinals in December.
Fleetwood stunned Premier League champions Arsenal on Tuesday, but Everton will fancy their chances of making the semifinals of a competition they have never won.
Everton have not lifted a major trophy since the 1995 FA Cup.
"I think the minute you use the word quarterfinals 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."