Ivan Cavaleiro put Wolves ahead in the 13th minute as he turned in Raul Jimenez's low cross, and for long stretches of the match they looked good value for the lead.
Rui Patricio in the Wolves goal did not have a huge amount to do, though he was helpless to deny Henrikh Mkhitaryan's curling late equaliser.
Nevertheless, Wolves continued to look a threat even after the leveller and struck the crossbar through Morgan Gibbs-White, while Adama Traore was denied by Bernd Leno.
But Nuno had only positive words to say about the promoted side at full-time.
"Coming to the Emirates and playing the way we played, I feel we should be proud," the former Valencia coach told reporters.
Big stage. Big performance.— Wolves (@Wolves) November 11, 2018
"It's a good point, but of course we could have won. We were organised, solid and brave to put our barriers in front of the ball.
"We stay humble, we came from the Championship and don't take our feet off the ground. Arsenal were not able to play the way they usually do so credit to the boys, they always covered and helped each other.
"When we had the ball we were threatening and created chances. The way we managed possession and created so many chances, against a very good team in a difficult stadium, is a credit to our players.
"It was an improvement from last Saturday, so let's work hard over the internationals and try to do better."
Leno played a key role for Arsenal and without him the Gunners arguably could have suffered a comprehensive defeat, and coach Unai Emery took note of the German's display.
He said: "We knew that today we needed the goalkeeper with his performance, because when we are taking risks in our attacking moments, and to give them a transition and options in the transitional moments, we would need the goalkeeper. I thought his performance was good for us."