The Toffees bounced back from their surprise midweek defeat to Crystal Palace courtesy of first-half goals from Leighton Baines and Kevin Mirallas to keep the pressure on Arsenal in the race for fourth place.
Martinez revealed that he was wary of United, who had the best away record in the league going into the match, but was delighted with how his side defended and hit the visitors on the break.
"We knew that we were facing a very good side. Away from home they have a terrific record and in that respect we had three games in eight days and it was important that we were focused and we were very clear in what we wanted to do and I think we did that," Martinez told Sky Sports News.
"We controlled the aspects of the game that we wanted to do. I thought we were electrifying on the counter-attack and I thought the way that we got in the final third was very enjoyable from that respect and then we worked extremely hard to keep a clean sheet."
The result means that Everton are now just one point behind fourth-placed Arsenal with three games left of the season.