Crystal Palace boss Ian Holloway has been fined ?2,000 after admitting a charge of improper conduct during the 2-2 draw with Leeds United.
Palace winger Wilfried Zaha has also accepted a similar charge after he was caught on camera making a gesture towards the travelling supporters at Selhurst Park.
Zaha has requested a personal hearing with the FA's disciplinary panel to argue his case.
Holloway was charged over comments he made to the match officials immediately after the final whistle.
The Eagles boss entered the pitch to confront referee Dean Whitehouse over his decision not to send off Leeds players Luke Varney and Stephen Warnock for perceived red card offences.
Holloway, who also exchanged words with Varney, admitted he went too far and has also said he will speak with Zaha about the incident.
"I was shouting that was wrong and I must be a role model. I will move on, as will Wilf," said Holloway.
"We are a well-run football club and we will deal with the issue concerning Wilf in the right way. I don't expect him to get a ban.
"There were incidents in the game that were not dealt with in the right way. That is now in the past and we have to get on with football."
The Scot celebrated 11 years in charge at Goodison Park on Thursday, but it has been one of the more difficult weeks of his tenure following the 3-0 home loss to the Latics in the FA Cup quarter-finals.
Moyes' contract runs out at the end of the campaign and earlier this season he indicated the Toffees' fortunes in the remaining games would play a big part in his decision.
With Everton out of the cup and facing a real battle to qualify for Europe, the speculation has grown that Moyes may opt for pastures new.
But the 49-year-old said: "It doesn't alter anything. The decision at the end of the season will be made by me and the players and how well we all do together, how high we finish in the league. It's never changed.
"I want the players to do well. You can see the way they've spoken this week, they're saying they're ambitious to finish as high up as they can, qualify for Europe if they can - well that's the same as the manager and that's what we're going to try to work towards."
Everton's fans vented their frustration at missing out on possibly two trips to Wembley, booing their side off at half-time and full-time.
The hostility was unusual but Moyes attributed it to expectations heightened by the impressive form his side have been in for much of this season.
He said: "I think the expectations have risen even higher. The team's performances this season have been the best football we've played in my time.
"The quality of the players, the style they've played in, the way we've gone about our job has rightly so put Everton at a level where the expectancy was that Everton have got a chance of top four, Everton have got a chance of winning one of the cups.
"When that doesn't happen then it's a big shock, but it was a big shock to us as well, we didn't expect it."
A section of fans focused their ire on midfielder Marouane Fellaini, who was jeered when he was substituted in the second half and then appeared to become involved in an altercation with supporters as he left the pitch and walked straight down the tunnel.
Moyes played down the incident, saying: "I didn't really notice any reaction at all. I think Marouane knew on the day his performance wasn't as good as it should have been. He's been great this season but on the day it just wasn't one of his best."
A visit from reigning Premier League champions Manchester City on Saturday has the potential for another difficult day for Moyes, but Everton's record against Roberto Mancini's side is impressive.
In seven previous games between the two managers, Mancini has picked up only four points, and none at Goodison Park.
Moyes referred to the protracted and fractious transfer saga that ended with defender Joleon Lescott moving from Everton to City in 2009 as a motivating factor for the Toffees and is desperately hoping their good run will continue.
He said: "We always found a little gripe with the Joleon Lescott thing a long time back.
"It wasn't too long ago there were quite a lot of similarities between the clubs. Obviously Manchester City are Premier League champions and have done brilliantly with the way they've moved their club forward, so you have to admire them for that.
"I don't think there's any reason (for the good record) but long may it continue and I hope it's the same this weekend."
Moyes, meanwhile, was delighted with midfielder Leon Osman's England call-up for World Cup qualifiers against San Marino and Montenegro - giving him the chance to win a first competitive cap.
The Everton boss said: "It's good that (England boss) Roy (Hodgson) has continued to pick him because he came in (to the England squad) at a moment where he was really in top form.
"It's been tough for Leon because for a lot of the season he's been the one who's carried the team. His performances have been excellent, whatever we've asked him to do, and he's come up with some important goals at times.
"He's had his best season for Everton, he really has been exceptional and I'm delighted he's got another call-up for England."
