Arteta said that was the correct decision, with Vieira given his marching orders after catching Josh Brownhill on the knee with his studs.
The praise from Arteta comes a week after he tore into the standard of officiating in the Premier League following Anthony Gordon’s winning goal standing in Newcastle 1-0 win over Arsenal.
Arteta and Arsenal have been contacted by the FA for their observations after the Spaniard’s rant.
But speaking after the win over Burnley, the Arsenal boss said: “Please ask me about VAR because today it was good.
“I hope that I’m on TV saying the referees are so good and I’m completely with them and being very constructive.”
Arsenal’s win moves them up to second in the Premier League and they are level on points with leaders Manchester City.
Leandro Trossard was the star of the show, scoring one and assisting another as the Gunners bounced back from two defeats last week.
“I think he (Trossard) connects everybody,” said Arteta. “He’s so intelligent.
“I think he moves in ways that attracts people that generates spaces and options for people.
“Today he did that really good because it was so difficult and the spaces were so small to attack. He gave us a lot of threat and possibilities to connect and find spaces for us.
“I think every time you ask him to play whether it’s wide or as a nine, it flows and he has a real threat. So I’m really happy with him.”
Arsenal secured the win without five first-team players, one of which was captain Martin Odegaard.
The midfielder has missed the past three games after picking up a knock in training on Friday last week and it is unclear if he will go on international duty with Norway.
“I don’t know,” said Arteta. “I am going to have a meeting now with the medical department and Edu to understand everyone’s situation but I think he is going to be back after the international break.
“I don’t know exactly what is the decision and the communication at the moment.”