Arsenal midfielder Vieira was sent off in the closing stages at the Emirates Stadium for a high challenge on Josh Brownhill.
It was the kind of flashpoint that could have provoked another angry reaction from Arteta.
The Gunners boss is waiting to discover if he will face a Football Association charge after he criticised the officials following last weekend's controversial 1-0 loss at Newcastle.
Arteta was asked to provide his observations to the FA having labelled Anthony Gordon's goal "embarrassing" and a "disgrace" after VAR gave it despite a clear foul by Newcastle's Joelinton.
But the Spaniard opted against any more rants, largely because the Vieira decision was hard to argue with and Arsenal took the win anyway to move level on points with leaders Manchester City.
"With the red card... yes, VAR was right," he said.
"The referee was right. Really good decision, really positive from Mikel to speak about that! Good decision.
"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."
Brownhill had cancelled out Leandro Trossard's opener, which ranked as Arsenal's 1,000th goal at the Emirates since their move from Highbury in 2006.
William Saliba headed Arsenal back in front before Oleksandr Zinchenko secured the points with an acrobatic volley.
Trossard was the difference-maker for the Gunners, the Belgium international once again starting as the central striker in the absence of the injured Gabriel Jesus.
Trossard also laid on the corner from which Saliba scored and it was another set-piece from the former Brighton star that led to Zinchenko's eye-catching scissor-kick.
"I think he connects everybody. He's so intelligent," Arteta said of Trossard.
"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.
"He put your body on the line if it's necessary, and that was it. It's the 1,000th goal at the Emirates - a beautiful number.
"I'm very happy with him. 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."
