The French forward came off the bench to net in his second consecutive Premier League match.
Eric Bailly had given United the lead on the stroke of half-time before the Red Devils added three goals in four minutes late on.
Romelu Lukaku followed up his impressive home debut by netting before Martial and Paul Pogba completed the rout.
Mourinho said: “Happiness in our play. It happened to me so much with my teams, you winning 1-0 and you can can concede. There was no need to close the door, just let the horses run freely.
“Anthony Martial is working hard. He is confident. The French language connection is there to help him a lot and get to the level we know he can be because the potential is huge.”
Manchester United: Team average – 7.71
“Anthony Martial is working hard. He is confident. The French language connection is there”
Manchester United boss Jose Mourinho
Mourinho also analysed the game and thinks United were good value for their lead.
He explained: “During almost 90 minutes, I don’t say 90 because there was a moment when they had a chance and we lost a little bit the confidence. They were waiting with class, calm and consistency for the moment to kill the game.
“Swansea played with five in the back and they had a moment when they felt they had to change and when they did we had more space and killed the game.
“I felt in control, if you had a chance to look at me and my body language I think you could see that.
“Football is football and when you make a mistake you can concede so I never felt totally relaxed. I had players on the bench who could help me.”