Martinez's charges became the first Toffees side to do the double over United in 45 years, and the Spaniard says that the win is testament to the "togetherness" flowing through the squad.
He told BBC Sport: "It was more than pleasing. It was an outstanding result and the first time we have done the double over Manchester United since 1969. I couldn't be prouder.
"We worked hard to keep a clean sheet, that is difficult to do when you take a two-goal lead, especially against Manchester United.
"It speaks volumes of the togetherness and focus of this team."
Consequently, the Merseysiders stay one point behind Arsenal in the race for Champions League qualification ahead of the remaining three fixtures of the season.