The 36-year-old was named on the bench against Vitoria, but kicked out at a fan and was shown a straight red, handed a season-long European competition ban and suspended by Marseille.
The former Manchester United man has been on the lookout for a club since the incident, and was brought to West Ham on a free transfer on Wednesday.
While he did not condone Evra’s actions, having spoken to the full-back, Moyes says he understands what happened, and has no concerns regarding the incident.
“No, not from what he told me,” Moyes told reporters.
“He told me what happened, none at all. It shows that he will stand up for himself and won't take anything. When he told me what the supporter said to him, I'd have had no complaints.
“No I wouldn't. But I think when you heard what the supporter said, you can understand it more.”
Despite not having played this year, Moyes, as he alluded to in his Standard Sport column, says there’s a chance he’ll be involved against Watford this weekend.
“Yes, there is a chance. He's not far away in my eyes as he has been training He played in November, he's no different from someone whose had a long injury so getting back playing quickly is the best thing you can do.”