Pardew apologised immediately after the match, and was fined £100,000 by Newcastle. The police have confirmed that they will not be bringing charges as neither Hull nor Meyler lodged a complaint.
Hull defender Alex Bruce has attempted to draw a line under the incident, insisting his team-mates just want to focus on their own game.
"It was obviously a huge incident and everyone has been talking about it but you just let the powers that be deal with that and see what happens," Bruce said.
"Obviously we understand that in the heat of the moment, things happen. I'm sure Alan regrets it.
"It's time to move on and put it to bed. It's happened and we've seen lots of incidents happen like that before, players doing things that they regret, and managers doing the same so you've just got to put it behind you and move on."
But the FA are expected to take a tough line with Pardew and he could be facing a long touchline ban and fine.
When the FA charged Pardew they said: ''Newcastle United manager Alan Pardew has been charged in relation to an incident in his side's game against Hull City on March 1, 2014.
"It is alleged that in the 72nd minute of the fixture, Pardew was involved in an incident with a Hull City player that amounted to improper conduct.
"Due to the serious violent and/or aggressive nature of the reported behaviour, this case has been designated as non-standard."
Designating the alleged offence as "non-standard" means there is no real precedent and that it cannot be treated in the same way as other more common disciplinary matters.
Referee Kevin Friend sent Pardew to the stands after the fracas, which occurred after Meyler had collided with the Newcastle boss while chasing a ball which had run out of play.
Newcastle acted swiftly to sanction their manager, issuing a formal warning on Saturday night on top of the heavy fine handed out.
"His behaviour was unacceptable and is not the behaviour we expect from the manager of Newcastle United," a club statement read.
"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."
Pardew had offered an immediate apology in the wake of the incident, but now looks set to face a heavy sanction from the game's governing body.
He told Sky Sports after Saturday's match: "It was just a heat of the moment thing. Obviously I massively regret it.
"I didn't mean to do anything aggressive, but I did move my head forward and that's enough.
"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.
Richard Bevan is pleased with how quickly Newcastle apologised after Alan Pardew headbutted David Meyler.
"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."
Meanwhile, Sky Sports pundit Alan Smith believes Pardew has sent out 'an awful message' to his players after his clash with Meyler.
The former Arsenal and England striker told Sky Sports News: "If he's behaving in that fashion how can he turn around and tell his players to toe the line on the pitch?
"It sends out an awful message and strangely he wasn't that sort of player. He never got involved in those things. So he's saved it all up until he became a manager.
"In the future he's got to keep himself out of these situations."