Everton are accustomed to bossing Premier League opponents, with their attacking philosophy based on being in control of the football.
They were however able to see off United on Sunday - earning them a first league double over the Manchester giants in 44 years - with their lowest possession stats of the season.
Martinez claims he set his side up aware that United would look to dominate and was delighted to see a different approach deliver an eighth win in nine outings.
Asked for the most pleasing aspects of Everton's performance, the Spaniard told Sky Sports: "I think it was the focus and the concentration, more than anything.
"We knew that we were facing a very good side, away from home they have a terrific record, and in that respect we have had three games in eight days and it was important that we were focused and very clear on what we wanted to do. I think we did that.
"We controlled the aspects of the game that we wanted to do. I thought we were electrifying on the counter-attack, the way that we got into the final third was very enjoyable.
"Then we worked extremely hard to keep a clean sheet. To get a two-goal lead, it is very difficult to keep a clean sheet because you are going to get Manchester United coming at you and throwing everything at you. I thought the manner in which we kept a clean sheet was very pleasing."
Martinez added: "Sometimes you need to adapt to what you are going to face on the pitch. We are capable of adapting to different things.
"I thought the way the game was going today, that suited us. When we need to be patient in our build-up and break teams down, we can do that.
"It was more the case with the amount of quality that United had on the pitch today, with the technical players that they had. It was a game that we had to be very solid and very well organised and use the dynamic football that we have.
"That was what put us in front in the game, gave us that two-goal lead."
First-half goals from Leighton Baines, who converted from the penalty spot, and Kevin Mirallas saw Everton past United and back to within one point of fourth-placed Arsenal in the race for UEFA Champions League qualification.
On that particular battle, Martinez said: "We are very clear with what we want to do.
"I was pleased that the team showed a real focus in wanting to win the game. I think the squad is ready, and that's pleasing.
"To take 24 points out of 27 is a remarkably consistent level and that's what we're going to do in the next three games.
"It's exciting. We have got a final game at home at Goodison against Manchester City and two very difficult fixtures away from home and we will try to get as many points as we can."