Pardew conceded he would be "stupid" not to expect the FA to come down hard on him in the coming days following the incident in his team's 4-1 Barclays Premier League win at the KC Stadium.
And Dyke told BBC Radio Five Live: "It looks serious and clearly we'll investigate - but there's nothing I can say about that."
Pardew was sent off in the 72nd minute of a contest his team went on to win 4-1, 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 for a throw-in.
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.
Yet 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."
The incident prompted bookmakers Ladbrokes to announce it has suspended betting on the next Premier League manager to lose his job, with a spokesman saying: "We wait to see how Pardew's actions are dealt with. Keeping the market open during games often keeps us on our toes but we've never come across circumstances like this to date."
Hull boss Bruce said: "He's apologised to us as a club and as far as I'm concerned the matter's over."
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, continued: "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?"