Pardew lost his composure in the 72nd minute of the encounter of the KC Stadium as he looked to move his head forward and strike Meyler, who had shoved the 52-year-old after going to collect a ball from the sideline.
The former West Ham boss' antics marred an excellent performance from Newcastle that ensured a first league win over the Yorkshire club since 1990.
Pardew is likely to face sanctions from the Football Association, who have already warned Pardew as to his future conduct after a touchline spat with Manchester City manager Manuel Pellegrini in January.
And Pardew was quick to apologise for his actions, insisting he did not mean to cause the former Sunderland midfielder any harm.
"It was a heat of the moment thing," Pardew is quoted by BBC Sport. "I massively regret it and I will have to sit down from now on.
"Of course, I didn't mean to do anything aggressive. I did move my head forward and that's enough.
"Perhaps I need to sit down from now on. It's a shame because it's taken the gloss off a terrific performance.
"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."
