Fulham manager Marco Silva and striker Aleksandar Mitrovic say they regret their actions and have apologised to referee Chris Kavanagh following their red cards at Manchester United.
Silva was charged with abusive behaviour towards match officials after the 3-1 FA Cup quarter-final loss.
Mitrovic, 28, was charged with violent and improper conduct after his straight red card for pushing referee Kavanagh.
"I should have controlled my own emotions better," said Silva.
In a statement, the 45-year-old Silva added: "I regret what happened, and I have spoken to Chris Kavanagh to apologise. He knows that I respect him and the job he has to do.
"Unfortunately, we did not see eye-to-eye on the day, but I recognise that he is one of the top referees in this country and I know that when our paths cross again, there will be mutual respect between us.
"I am sorry that I was not on the pitch to try to lead the team to what could have been an historic FA Cup semi-final at Wembley, but I am thankful for all the support I have received from Fulham fans over the last few days."
Serbia forward Mitrovic is facing a lengthy ban after the Football Association said its standard punishment for his sending off at Manchester United was "clearly insufficient".
He said time away with his national side had allowed him time to reflect on the match at Old Trafford, in which he was dismissed for pushing referee Kavanagh as he protested the awarding of a penalty either side of red cards for Silva and team-mate Willian.
Fulham had led 1-0, but they collapsed after Silva was sent off as Kavanagh reviewed the penalty for handball - which led to Brazilian Willian also being red-carded before Mitrovic angrily remonstrated.
With an apology to his team-mates and the club's supporters, Mitrovic said: "On a personal level, I regret my actions that led to me being sent off.
"I allowed my frustration to get the better of me, and how I reacted was wrong.
"I was trying to get the referee's attention, but I appreciate that I should not have put my hands on him and I understand why he showed me a red card, my first in-game sending off for Fulham and my first since the 2015-16 season.
"I have accepted the three-match ban for my red card, I have spoken to Chris Kavanagh to apologise, and I have volunteered to accept a club fine.
"I now want to do what I can to put this incident behind me and get back to helping my team-mates on the pitch as soon as possible."
In addition to an improper conduct charge for allegedly throwing a water bottle in the direction of the assistant referee, Fulham boss Silva has also been charged with misconduct for comments he made following the FA Cup defeat.
The FA alleges his post-match comments "constitute improper conduct, in that they imply bias and/or question the integrity of the match official, and/or bring the game into disrepute".
Fulham also face a further charge of failing to control their players at Old Trafford.
Mitrovic would typically face a three-match suspension for a straight red card for violent conduct, however, that ban can be extended depending on the circumstances.
Former Premier League striker Chris Sutton called for Mitrovic to be given a 10-match ban - which was aechoed by former referees' chief Keith Hackett - but boss Silva appealed for "fairness" from the FA.