Wolves were taken into extra time before Bright Enobakhare converted a Barry Douglas cross in the 98th minute to send the hosts through.
Happy with the result, Nuno admitted it was a tough game but says he is happy to progress to the next round.
He said, “The result of course was important as it’s a good competition and we go through - that's the main thing that we get there.
“Bristol played well - it was a tough game, in these cup games there are no divisions.
“There are good teams that come and fight like Bristol did - fortunately we are able to go through but we give credit to them. They did well, they had good chances - it was a tough game.
"There were good things and bad things – in the first half we had a good game and did o-k but not so good in the second.
"It was difficult with players coming in and coming back from injury.
"It was good to get minutes for some players getting back in shape as we continue our fight."
In a game in which both sides had chances to win it, Wolves had Will Norris to thank for a number of fine saved.
Nuno was happy with the performance of his goalkeeper but credited the team for a strong defensive display.
“The team did it, Will (Norris) did his job, he did well and the team defended well. There was a lot of cooperation between the boys and the clean sheet is good for us.
“Scoring will give Bright (Enobakhare) some confidence and it has shown him that he has to work.
“He has been a very important player this season and now he’s come back again - we know that all of the players in the squad are very important to us.
“The Under 23 boys gave us a hand - Oskar (Buur Rasmussen) starting as well, it’s important.
“It’s a group, it’s a squad , it’s players that want to help the team this is the most important thing for us. I’m happy with that.
“We only look as far as tomorrow. Tomorrow is the day that we are thinking about as we prepare for the game on Saturday at Molineux - it's a very important game for us.”