Gervinho was dismissed for slapping the Magpies midfielder after Barton had grappled with the Ivory Coast international.
Barton, 28, felt that Gervinho had gone down too easily under a challenge from Cheick Tiote.
"Merely called out a fellow professional for blatantly cheating. Everyone hates a cheater," Barton wrote on Twitter.
"What do you want me to do? Stand and trade blows with Gervinho? If you raise your hands to a player's faces you should be off. The ref got it right.
"I train all summer to have him cheat us out of a hard earned point. It's not on. Diving should be a three game ban."
The match ended in a goalless draw.