The incident, which came in the 72nd minute as Meyler sought to retrieve the ball from behind Pardew at a throw-in in front of the dugouts, cast a shadow over a match the Magpies went on to win 4-1.
Football Association chairman Greg Dyke has confirmed the organisation will investigate the incident, while Pardew himself conceded he would be "stupid" not to expect the FA to come down hard on him in the coming days.
In a statement released late on Saturday night, Newcastle said: "Newcastle United are disappointed with the actions of its manager Alan Pardew this afternoon. His behaviour was unacceptable and is not the behaviour we expect from the manager of Newcastle United.
"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 Barclays Premier League.
"Sadly, the headlines tomorrow will not be focused on the result or the efforts of the players, but instead on the actions of our manager.
"Alan unreservedly apologised immediately following the game to the player, to Hull City Football cub and its fans, and to the fans of Newcastle United.
"We have held discussions this evening with Alan who has offered his sincere apologies to the club and it is clear he deeply regrets his actions. Alan has accepted a formal warning from the club in relation to his behaviour today and also a club fine of £100,000.
"The club is now drawing a line under this matter and will be making no further comment."
Pardew was sent to the stands and Meyler shown a yellow card following their clash which occurred with Newcastle 3-1 up, referee Kevin Friend adjudging the Magpies boss to be the main aggressor in an ugly tussle sparked when Meyler barged into the 52-year-old while attempting to retrieve the ball.
Pardew, no stranger to touchline altercations in the last year with his confrontation with Manchester City boss Manuel Pellegrini the highest profile, appeared to move his head towards the former Sunderland midfielder, who was later commended by Hull boss Steve Bruce for not making more of the contact.
While the Republic of Ireland international midfielder's actions perhaps warded off an even more explosive melee, Pardew admitted he had crossed a line.
He said: "He was right on top of me and I wanted to just ease him away from me but obviously I put my head in a forward motion. I want to apologise to him, everyone at Hull and obviously my own fans as well.
"I don't think it was a headbutt. It wasn't a motion that was quick.
"Sometimes when you're on the sideline like that you can get involved in a moment like that. It was an incident that just flared up all around me. I just wanted to get him away, but with the forward motion...you can't do that.
"Of course, I'm not stupid enough to accept there's going to be no punishment. I'll have to accept whatever comes my way.
"I believe my behaviour over the years has not resulted in too many fines and sitting in the stands, but this one probably will."
The incident took the gloss off a superb display by the Magpies, who had been goal-shy in recent weeks but exploded into life on Saturday thanks to a Moussa Sissoko brace and one each for Loic Remy and Vurnon Anita.
Pardew's antics will generate yet more negative headlines for a club never far from controversy for one reason or another, and the manager admits Saturday's episode may well be a personal watershed.
"Definitely from now on I'm going to sit down and stay out of the way. I'll have to sit in the dugout - hopefully I'll be in the dugout, we'll have to wait and see," he added, alluding to the likelihood of an FA ban.
"I want to win games. Perhaps I get too involved in it by standing so close to the action. The thing today has told me to go and sit down, watch the game and keep out of the way.
"Sir Alex Ferguson once said to me, 'go and sit down'. I think he was probably right."
Hull boss Bruce felt Pardew would have instantly regretted his rash reaction.
"He's apologised to us as a club and as far as I'm concerned the matter's over," said Bruce, whose charges pulled back to 2-1 early in the second half through a Curtis Davies header but failed to kick on from there.
"I've never seen or witnessed anything like that. There's no question that Alan's led with his head and he's obviously lost it. I'm sure Alan will regret it and he'll look at himself later on and think 'what the hell have I done?'
"I don't think I've ever seen a manager do anything like that. We're all in a state of shock. It's for Alan to live with and deal with the consequences.
"I'm sure he'll regret his actions for a long time. I would imagine Alan would be in serious trouble, serious trouble."
Bruce was at least able to joke that Pardew was fortunate Meyler did not respond in kind.
"He's lucky that he didn't get one back! Then he would have been in serious trouble," he said.
"A 25-year-old against a 50-year-old is a mismatch, isn't it?"
Pardew's actions were also savaged by pundits.
Match of the Day's Alan Hansen said: "There's outrage and understandably so. It's terribly sad to see these pictures, sad for Pardew, sad for Newcastle and sad for the game.
"Meyler doesn't do a lot to provoke him and yet he still lost it totally. The pictures are very, very bad."
BBC Radio 5 Live pundit Robbie Savage questioned whether the Newcastle manager's position had become untenable as a result of the incident.
He said: "I think it's a shocking act. A ridiculous, scandalous act from a manager who's got previous. Has his position become untenable?
"It's violent conduct, a three-game ban for a player. Because it's a manager I feel it's worse. He's been sent to the stands.
"I would give him a complete ban from now until the end of the season...home and away games.
"But given Newcastle's current position (safe from the threat of relegation), is that any punishment?"
Former England international and Match of the Day presenter Gary Lineker took to social media to say: "Inexcusable from a manager."
Another pundit, Richard Keys, added on Twitter: "Sir Bobby Robson will be spinning in his grave."
Former Tottenham and Liverpool midfielder Jamie Redknapp said Pardew's conduct was "unacceptable".
Now a pundit on Sky Sports, the 40-year-old said: "It's absolutely unacceptable. You don't go to headbutt someone - that's not right.
"You have to set standards as a manager, you're a representative of your club. It's extremely wrong."