Martial’s curling finish added to Paul Pogba’s first-half penalty as Mourinho’s side held on to move above Everton in the league, despite Gylfi Sigurdsson’s late goal from the spot.
The French winger is reportedly continuing to negotiate a new contract with the club and his latest performance, to extend a run of good games for the 22-year-old, may prompt United to wrap up a new deal.
When asked by Sky Sports, Mourinho said Martial has most improved at “everything”.
“He has the same natural talent that he had one or two years ago but he is improving his way of thinking football, thinking training too, and thinking his role in the team.
"I am really happy with him, Luke Shaw, boys that are improving. They had difficult periods, difficult periods for myself, because I want more from them and I took them to the limits. But in this moment I think both, and in today's case Anthony, was able to do things he was not able to do before. So really, really happy with Anthony."
Mourinho’s side were under pressure heading into the game on the back off the home Champions League defeat against Juventus, but the manager has taken some pride in his players’ performances at the weekend.
"When the players are playing bad, when the players are playing well it's my responsibility. Or, we go to the middle, which I think is fair, and say when a player plays bad it's half me, and half the player, and the same when a player plays well,” he said.
"I think he coped well with this development process. He took quite a long time to understand what we want from him, took quite a long time for his brain, and also his body, to be ready to play the way we want him to.
"But at the moment he is solid, playing very well, and even if he doesn't score, his performance is a solid performance for the team, and that's what we need. So I'm very happy with Anthony."