The Magpies boss was fined and formally warned by his club in the wake of the incident, while the Football Association have also handed him a seven-game ban
The 52-year-old sparked controversy during his side's 4-1 victory at Hull on March 1 when he clashed with Meyler on the touchline.
Pardew has since been handed a three-match stadium ban and four-game touchline suspension by the Football Association (FA), with the former starting against Fulham on Saturday.
Newcastle formally warned Pardew and fined him £100,000 (€120,000) in the immediate aftermath of the incident, but opted not to dismiss the former West Ham boss.
Speaking in his first press conference since learning his punishment from the FA, Pardew thanked his club for the backing they have given him.
"It was a relief when I was told I would not lose my job," he said. "My mistake was in front of millions of people and I had to pay a price.
"[Owner] Mike Ashley acted swiftly and we move forward. Since the incident, the backing I have had from the club has helped me."
Assistant manager John Carver will take charge against Fulham on Saturday, and Pardew insisted that Newcastle are fully prepared for their visit to the relegation-threatened club.
"Our game plan is in place. John Carver knows it inside-out and I trust him 100 per cent to deliver it," Pardew added.
Captain Fabricio Coloccini is poised to rejoin the first team after missing the win at Hull due to a family bereavement, a return that Pardew feels will be key in helping the team manage his absence from the dugout.
"Coloccini will come back into the team and he is important," Pardew explained. "His captaincy needs to step up a level over the next three games."