First-half goals from Scott Golbourne and Kevin Doyle put Wolves on course to secure five straight league wins for the first time since 2008.
But Swindon created a host of chances, being frustrated by goalkeeper Carl Ikeme, before Dany N'Guessan struck in the 82nd minute.
Kevin Foley then restored Wanderers' two-goal advantage before Ryan Mason struck from long range in a tense finale.
"I am absolutely delighted with the performance," beamed Cooper. "I feel desperately sorry for the players as they did not deserve to lose the game.
"I think they totally bossed the game from start to finish and that is not being disrespectful to Wolves. I just felt that we totally out-footballed them and deserved to win the game.
"I said to them that if they can guarantee me that level of commitment and desire then the performances will keep coming and if you keep performing well then you get consistent results. The only criticism I have got is that we are conceding too many soft goals.
"A number of times we hit the target and the way that we have played to create those chances is unbelievable. I think everyone appreciates what a good football team we have got. It was a fantastic performance.
"Yes, you are upset about the result, but the performance was out of the top draw. They showcased their talent and I just wish they had got a result which was deserved."
Wolves quickly took control of affairs but there was some good fortune about Golbourne's first goal for the club following last month's B£700,000 move from Barnsley.
His third-minute high ball into the box was meant to be a cross but it drifted towards goal and completely deceived keeper Wes Foderingham, who was left somewhat embarrassed as the ball drifted over his head and into the corner of the net.
Swindon could easily have wilted after that early setback but it was they who then dominated proceedings only for Mason and Alex Pritchard to be denied by Ikeme.
Failure to convert their chances cost Swindon dearly two minutes before half-time when Doyle released Leigh Griffiths and then raced into the area to convert a cross from the Scotland international with a far-post header.
Mason then failed to take any of three gilt-edged chances that came his way in a six-minute second-half spell - including one that hit the post - before N'Guessan showed him the way to goal, ironically from a pass by Mason.
Foley then looked to have made the game safe when he met a cross from Bjorn Sigurdarson, only for Mason to set up a thrilling finale with an unstoppable 30-yard drive.