Riccardi Calafiori hit the winner for Arsenal after Myles Lewis-Skelly was sent-off for the visitors before halftime. Joao Gomes was also dismissed for Wolves midway through the second-half.
Arteta said: "I'm extremely proud of the players. You can talk about our courage, you can talk about spirit and intelligence. The way they managed the game emotionally was unbelievable, especially with what we had to face and they just faced the situation and the challenge.
"We went into the second half and the only message was to go out there and win the game. That's it. They did it and in a really convincing way to deserve to win the game."
On the red card, he continued: "I think it's that obvious that we don't need any comments today. Hopefully the right thing will happen after today.
"If we have to (appeal), it's a really good precedent with what happened with Bruno (Fernandes vs Tottenham) this season. Hopefully.
Ok we were in a position we shouldn't have been in, at least let's be in a position that we should be in for the next few weeks and allow our player to continue to do his job.
"This season has been very special for many circumstances, a lot of them very challenging. Today we had two again with Mikel (Merino) and Martin (Odegaard) out.
"Still we come here, we have to face a very difficult opponent fighting for relegation and we have another issue during in the match, but still we go about it and that's what I love about them. That's why our supporters as well celebrated and they were behind them because they can feel that.
"We put so much work, hours, passion and dedication into what we do that regardless of what happens and what is thrown there, you have to continue to have that desire and that will to win and overcome the situation and not throw it through the window.
"It's my job, our job, to deal with certain things and unfortunately we're getting used to it."