Newcastle United have fined manager Alan Pardew £100,000 and given him a formal warning for headbutting Hull City midfielder David Meyler.
Pardew, 52, was sent to the stand for the incident during the second half of the Magpies' 4-1 win at the KC Stadium.
"We have held discussions with Alan, who has offered his sincere apologies," said a club statement. "It is clear he deeply regrets his actions."
The Football Association has said it will investigate the incident.
Former FA executive director David Davies said it was difficult to forecast the length of any potential suspension but told BBC Radio 5 live's Sportsweek programme on Sunday: "I think it will be a serious punishment."
Asked if he thought a 10-game ban until the end of the season was a possibility, he said: "That's conceivable".
With the Magpies 3-1 up, Pardew was angered when Meyler shoved past him in an attempt to retrieve the ball to take a throw-in.
The pair came together, with the former Reading and Southampton boss pushing his head into the face of the Hull player.
A fracas involving players and staff from both sides followed and, when the crowd was dispersed, Meyler was booked and Pardew sent from the touchline.
Speaking after the match, Pardew said: "I did not mean any damage to the guy but I have moved my head forward. I tried to push him away with my head.
"I apologise to everyone. I should not have got involved in it.
"I don't think it was a headbutt. It wasn't a motion that was quick."
In their statement, released six hours after Saturday's game ended, Newcastle said Pardew's actions were "unacceptable" and "not the behaviour we expect from the manager".
The club added: "It is most disappointing that this incident has taken the focus away from what was a fantastic performance by the team and an excellent result away from home which leaves the club in eighth place in the Premier League."
BBC pundits Alan Hansen and Robbie Savage condemned Pardew's actions.
"The pictures are very, very bad," said former Liverpool defender Hansen on Match of the Day.
"There was outrage and understandably so. There was not a lot of provocation, Newcastle were 3-1 up and absolutely cruising.
"The only ones who can sack him are Newcastle and they've taken the view to give him a massive fine and warn him.
"He's a lucky, lucky man. I don't know what he was doing getting involved in the first place."
Savage, also speaking on Match of the Day, described Pardew's actions as "disgusting".
The former Wales international had earlier told BBC Radio 5 live Pardew should be given a 10-game stadium ban.
The Newcastle boss, who in 2012 was given a two-game ban for pushing an assistant referee, admitted his behaviour had "taken the gloss off a magnificent performance from my team" and said he was "very upset" with himself.
FA chairman Greg Dyke told BBC Sport: "Clearly it looks serious and we will investigate it but I can't really say anything else at this stage."
Hull boss Steve Bruce sympathised with his Newcastle counterpart because of the "pressure" managers are under, and also praised Meyler for staying on his feet.
Bruce told BBC Radio 5 live: "I'm sure Alan's absolutely regretting it and questioning himself, asking 'how the hell have I done that?'.
"The pressure on all Premier League managers is enormous. It's not like Alan, he's an established Premier League manager.
"I'm delighted with the reaction of David Meyler because other people would've been rolling round the floor. We've all done silly things in the heat of the moment."
In January, Pardew said sorry after television cameras caught him verbally abusing Manchester City manager Manuel Pellegrini during the Magpies' 2-0 defeat at St James' Park.
In November 2006, he apologised to Arsenal manager Arsene Wenger for his celebrations following a winning goal against the Gunners, some eight months after he denied Wenger's claims he was a racist or xenophobe.