Pardew's situation looked desperate, and Alan Shearer has called on the Newcastle manager to be sacked, but Ashley is standing by his man.
The FA will come down hard on him in the coming days but they cannot demand Newcastle replace him.
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 a tough punishment.
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 Club 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."
As always, NOBODY from NUFC will stand up and face the media.
It's the usual - "we do it our way - we tell you what we want you to hear - Mike Ashley is not accountable to anyone. This is a business - not a football club."