Pardew was dismissed for the incident during the second half of the Magpies’ 4-1 victory at the KC Stadium.
The 52-year-old said: “I did not mean any damage to the guy but I have moved my head forward. I tried to push him away with my head but I should not have done that.
“I apologise to everyone. I should not have got involved in it.”
With the Magpies 3-1 up, Pardew was angered when Meyler shoved past him in an attempt to retrieve the ball to take a throw-in.
The pair came together, with the former Reading and Southampton boss pushing his head into the face of the Hull player.
A fracas involving players and staff from both sides followed and, when the crowd was dispersed, Meyler was booked and Pardew sent from the touchline.
The Newcastle boss, who in 2012 was given a two-game ban for pushing an assistant referee, added: “It was a situation where I should not have been there.
“I will sit down from now on and send [assistant manager] John Carver out there.”
Pardew admitted his behaviour had “taken the gloss off a magnificent performance from my team”.
He added: “The players were terrific; it was only myself who had a poor performance all-round. I am very, very pleased with the team but very upset with myself.”
Shortly after full-time, but before Pardew apologised, a leading bookmaker suspended betting on the next Premier League manager to be sacked.
Hull boss Steve Bruce sympathised with his Newcastle counterpart because of the “pressure” managers are under, and also praised Meyler for staying on his feet.
Bruce told BBC Radio 5 live: “I’m sure Alan’s absolutely regretting it and questioning himself, asking ‘how the hell have I done that?’.
“The pressure on all Premier League managers is enormous. It’s not like Alan, he’s an established Premier League manager.
“I’m delighted with the reaction of David Meyler because other people would’ve been rolling round the floor. We’ve all done silly things in the heat of the moment.”
Written by Steve Milne
Follow me on Twitter: @stevenmilnelive