The contest saw Zaha react in animated fashion to some challenges made on him, including briefly squaring up to John McGinn and protesting to referee Chris Kavanagh.
The Ivory Coast forward was taunted by Villa fans and at one point in the second half cupped his ears to the crowd.
When asked in his post-match press conference about Zaha’s behaviour, Vieira said: “This is part of Wilfried and his character, his personality.
“This is a strength, (and) weakness at the same time. I think at times there were some fouls, and he is a target player, of course. But he has to manage the situation.
“He has to manage his mind, he has to keep that energy, that strength to allow him to make those kind of differences in the last third. This is something he will have to manage better.
“Saying that, he is a target, and I think it has been a bit difficult for him at times.”
Palace secured a point through a close-range finish by substitute Jeffrey Schlupp in the 81st minute that cancelled out Ollie Watkins’ 69th-minute opener.
Watkins got his boot on the end of a Lucas Digne cross as he tussled with Marc Guehi at the far post.
Vieira questioned the decision to allow Watkins’ goal to stand, saying: “From where I was I thought it was a foul. There is a player who plays the ball and other ones who play the player. But I didn’t have the chance to look at it again, so that was from the angle I was.”
The Frenchman, who revealed Michael Olise had missed out with an injury that will keep him sidelined for the remaining two games of the season, added: “I’m really happy with the performance.
“It wasn’t easy to concede that goal. I think we didn’t deserve to really concede that goal, and we showed quality and character to fight and to find the strength to get back in the game and score.”
Villa boss Steven Gerrard said when asked about Zaha’s antics: “It’s a sideshow at the end of the day. He had a really quiet afternoon, I thought we dealt with him extremely well. That’s the main thing and the only thing I’m concerned about.”
Regarding Watkins’ goal, Gerrard said: “Those duels and challenges were getting played on all over the pitch. I didn’t see any reason why it should have been ruled out and Ollie deserves all the credit for that goal.”
Villa’s attempts in the first half included Danny Ings sending a trio of shots off-target.
And Gerrard – whose side stayed 12th in the Premier League, one place behind Palace – said: “I think on another day if we were more ruthless and clinical we would have been sat here talking about three points rather than one, (and we were) really naive in terms of the goal we’ve conceded, but our overall performance, I don’t think there was too much wrong with it.”
Gerrard also said he would be “extremely surprised” if Ezri Konsa plays again this season after the defender limped off early in the second half having sustained “an issue in the knee area”.