The extraordinary second-half flare-up happened when Hull midfielder David Meyler barged into the Newcastle manager as he looked to retrieve the ball for a throw-in.
Pardew, no stranger to touchline altercations, then squared up to the former Sunderland midfielder before appearing to move his head in the direction of the Irishman.
Pardew, who in 2012 was given a two-game ban for pushing an assistant referee, said: "It was a heat of the moment thing, I massively regret it."
Pardew, who has had touchline altercations with Paolo di Canio, Mauricio Pochettino and Manuel Pellegrini in the last year, added: "I think I'm going to sit down now because that's two or three incidents I've been involved in. I think I'm going to sit now.
"I didn't meant to do anything aggressive, but I moved my head forward and that's enough.
"It's a shame because it took the gloss off a fantastic performance from us. That's upsetting."
Referee Kevin Friend sent Pardew to the stands and the FA are now sure to take action.
Shovelling salt into the wound, Ladbrokes last night suspended betting on the next Premier League manager to lose his job following the incident.
Hull boss Steve Bruce refused to condemn his fellow manager over the square-up. He said: "I think Alan knows he's been stupid and apologised.
"In the heat of the game we all do silly things and I think he regrets it. It's a game with emotions, but it's gone, as far as we're concerned. We've accepted his apology."
Bruce added: "I'm pleased with David Meyler's reaction too. If he'd rolled around on the floor it could have been a much bigger incident."
Hull had been aiming to do the double over their adversaries, having beaten Newcastle 3-2 in September.
But the feelgood factor at the KC stadium disappeared within 10 minutes when Mathieu Debuchy tore down the right and his low pull-back was met with a sweet first-time effort from Moussa Sissoko to put Newcastle in front.
Hull then found themselves two behind at the break when Maynor Figueroa inexplicably under-hit a backpass which was seized upon by Loic Remy, who rounded McGregor before slotting into an empty net.
Hull needed a speedy response at the start of the second half and that is what they got as they immediately pulled one back.
Tom Huddlestone's free-kick was delivered into a crowd of players on the edge of the six-yard box, with Curtis Davies hanging in the air and nodding beyond Tim Krul who got a fist to the ball but could not keep it out.
Yet Hull's hopes of a fightback were dashed within moments, a loose touch by Huddlestone in midfield inviting Sissoko to lead the breakaway.
His pass picked out Yoan Gouffran who drilled a low shot that was only parried by McGregor, and it was Sissoko, smartly continuing his forward run, who lapped up the rebound.
Hull struggled to mount a response in what time remained and Newcastle saw Remy and Gouffran both go close to adding to the scoring before Vurnon Anita added a fourth in injury time.