The win at Old Trafford was the Blues' first for 21 years and Martinez talked up his players' display after the game.
"I'm very proud of my players," Martinez told Sky Sports News.
"To come here and play with the arrogance they showed is very pleasing for me.
"They played their stuff and always tried to keep it that way, so I'm very pleased to see this kind of performance."
Martinez's side are now fifth in the Premier League.