Pardew was sent to the stands after his confrontation with the former Sunderland midfielder in the 72nd minute of the game with replays showing the Magpies boss leaned in with his head after Meyler had brushed past him to retrieve the ball.
At the time, his side were 3-1 up and controlling the game and Pardew was quick to apologise for his actions.
“I think I’m gonna have to sit down from now on,” said Pardew, who is likely to face action from the Football Association for the incident.
“It was just a heat of the moment thing. Obviously I massively regret it. I think I’m gonna have to sit down from now on because that’s about two or three incidents I’ve been involved in on the line.”
Earlier in the season, Pardew was warned of his future conduct by the FA after shoving a linesman during his side’s 2-1 over Tottenham at St James’ Park.
Then, In January Pardew escaped punishment over a foul-mouthed rant at Manual Pellegrini.
“That’ll be me sitting down from now on as a manager. Yeah, of course (I crossed the disciplinary line). I didn’t mean to anything aggressive or anything, but I moved my head forward and that’s enough.
“Of course I apologise. I represent a big club.
“I tried to push him away with my head and I shouldn’t have done that. My team were terrific and it’s only myself who had a poor performance.”
Former Newcastle manager Graeme Souness and former captain Alan Shearer, who were working as pundits on the game for BeIn Sport, both suggested Pardew's position was untenable after the incident.