Bryan Oviedo hit a late winner at Old Trafford last night.
Everton have been beaten only once in the league this season and currently lie fifth in the table, three points off second place.
And on the Toffees ending their 21-year Old Trafford hoodoo, Martinez said: "Today was more than a football game for us - it was about trying to get over the mental block that we have had for many, many years.
"Someone told me was 20-odd years since we won at Old Trafford.
"It was about being ourselves throughout the game. I couldn't be prouder.
"The performance is not by any means our best of the season, but we had a real mentality in the first half when we had to dig in, when Manchester United created a few chances as you would expect.
"We never felt inferior.
"I have always felt this squad is capable of going anywhere in this league and playing teams eye-to-eye.
"In the first half we did certain good things. The second-half performance was a lot better and when we had to defend, we did, when we had to keep the ball, we did, and when we went into the final third we had real composure and looked a real threat.
"I told the boys afterwards that this gives a real indication of what can be achieved.
"But we have done nothing - we need to carry on improving, carry on getting better."
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