The Canaries were trailing to a deflected Jermaine Johnson goal when Mooney bundled the ball home from close range after 83 minutes, after substitute Alan Lee had headed a deep cross back into the danger area.
Norwich's celebrations were cut short when referee Mike Russell penalised youngster Korey Smith for a push on goalkeeper Lee Grant and Gunn was furious with the official after the game.
"I hate coming in here and talking about referees. It just seems to be happening too often, especially here at Carrow Road," he said.
"Once again the supporters were singing about the referee afterwards.
"I waited my 30 minutes and then had a word with him about the decision and he said he had disallowed the goal for a push, but we all feel very harshly done by over that because our players thought it was a goal and their players weren't complaining either.
"In fact one of them handled the ball on the line to keep it out so he clearly didn't think there was anything wrong with it.
"It just seems to me that teams at the bottom end of the table don't get the rub of the green but there is nothing we can do about that now."
Gunn was determined to look on the bright side though, despite seeing his team drop to fourth from bottom in the table.
He said: "There was no ranting and raving in the dressing room afterwards because we need the players to believe that we can get enough points between now and the end of the season to ensure our safety.
"We've got to remember that we've had a very good return of 10 points from our previous five games and now we've got to make sure we take as many points from our final five games as possible."
Gunn, despite being disappointed with the disallowed goal, conceded that his side fell below the standards that had seen them win their previous two home matches and take a point from a testing trip to Birmingham last time out.
He said: "To be honest we didn't play well in the first half, while at the same time Sheffield Wednesday played some relaxed football.
"I always knew it was going to be a tough game and that's just the way it's turned out.
"After the break I didn't think there was much in it but unfortunately they've had a shot which has taken a deflection to beat our goalkeeper.
"David Marshall made a brilliant save in the first half to prevent them going ahead and I'm sure he would have saved that one as well if our player hadn't got a touch on it.
"But having said all that it was poor defending on our part for letting him get a shot in in the first place.
"After that I thought we did well and as I've said we would have got a point for our efforts if it hadn't been for that decision by the referee."
Wednesday manager Brian Laws felt his side were well worth the three points.
Laws said: "We have been exceptionally good in our last four away games and deserved to win all of them in my opinion.
"Today was no different and this time we got our just rewards. We dominated the first half, passed and moved really well and had 10 strikes on goal.
"We got our goal early in the second half and then had a little bit of luck towards the end but overall I don't think anyone would disagree that we deserved to win.
"We went out there and proved that we've got no intention of switching off just because of our position.
"Now we know we won't be going down and we won't be going up either but I want the players to drive forward and finish as high as they possibly can to give everyone plenty of optimism for next season."
As for the disallowed goal, Laws added: "It's difficult to see what happened from pitch level and I've no idea why it was ruled out.
"All I could see was a melee of bodies and in those sorts of situations the referee often tends to lean towards the 'keeper's side. We have probably had a little bit of luck go our way.
"I just hope Norwich don't go down. They are a good club."