Nuno's side fell to a 2-1 defeat at Turf Moor, with Ashley Barnes and Chris Wood scoring for the hosts before Fabio Silva's late reply from the penalty spot.
It was a poor performance from Wolves but the Portuguese, who has been reluctant to comment on referees in the past, was firmly focused on Mason afterwards.
"The referee does not have the quality to whistle a game in the Premier League. This is a problem that we knew – we had Lee Mason before," said Nuno.
"It is not about the crucial mistakes or decisions, it is about the way he handles the game. The players get nervous, too much voices, he whistles by the voices when some players are shouting.
"We are talking about the best competition and clearly he doesn't have the quality to whistle the game.
"I'm very disappointed to say this but I would not feel right if I didn't say it.
"I just don't want to see him more – that's what I told him. I hope he doesn't whistle a game of ours again because all the games we have with Lee Mason are always the same.
"He cannot control the players, the players are constantly arguing – both teams. With all the other referees the game flows, there's dialogue. He's just not ready to do it."
Wolves failed to keep up the momentum after their comeback victory over Chelsea last week, with Burnley deserving the victory despite Silva's first senior goal in gold and black making for a nervy finish.
When asked about the performance, Nuno said: "It was a tough match and we expected a tough match.
"We started the game well, but we conceded in a poor way with both goals.
"Second half, we started well. But it's disappointing the way we conceded the goals.
"We should have a better answer for this situation.
"It was a tough game. The way we conceded is something we should have done better, but there were also good things.
"We started well in possession, breaking and going forward.
"We should have finished more actions, even in the second half when Burnley dropped.
"We were not able to create too much. It requires dynamic actions.
"We should have had more speed on the ball, and improve that for the next one."
The positive of the night was substitute Silva's well-taken spot-kick, opening his account after his £35million move from Porto in the summer.
"There are positives from the game, young players who are starting to grow in such a hard competition," said Nuno.
"This moment for Fabio is important. He got the penalty, and he scored it well. It's good for his confidence."
Owen Otasowie, meanwhile, made his first top-flight start in an unconventional false nine role after his impressive display off the bench against Chelsea.
The young American was substituted on the hour mark, and Nuno added: "I think he did well. He's a young player, very young, and making his first steps in the high level of competition.
"I think he handled himself pretty good. There a lot of aspects we have to improve, but he has talent."