Martinez said: "I thought it was going to be a very difficult game and it proved to be.
"I thought Norwich were very brave, playing with two strikers to try to hit us on the counter, so I thought we balanced that really well.
"The amount of opportunities we had, the clinical touch in front of goal was probably missing.
"But when Norwich had a proper go in the second half, we defended well and we kept an important clean sheet.
"I thought we controlled the game really well and we got three important, and well deserved, points.
"Some phases of our game were fantastic and some of the play we had was electrifying."
The result ended a positive day for the Toffees after they completed the signing of former Celtic star Aiden McGeady.
Martinez's men were also back above neighbours Liverpool - at least for one night - in the Champions League places.
The Spaniard, however, insists he is not yet looking at the league table.
He said: "In the league I like to work towards the last third of the season and when you go into the last nine games of the campaign that is when you get the significance of every point, of where you are in the table and how the results affect your position.
"At the moment we are still just trying to get as many points as we can."
Norwich struggled to make an impression in the game until belatedly starting to make some headway when already 2-0 down in the final half-hour.
They did create some chances but the closest they came was when Robert Snodgrass headed against the post.
The Canaries are now without a win in the league in seven matches but manager Chris Hughton denied he was feeling any extra pressure.
He said: "There is always pressure on managers at whatever stage of a season.
"We want to win games and football matches. There is no greater pressure on myself at this moment than there has always been."
But with his side slipping towards the relegation zone, Hughton accepts results need to improve.
He said: "Yes, very quickly. That is something we are aware of.
"With how the league is we need to start winning games and that means scoring goals.
"I take pride from the fact in the last half-hour we made a real good game of it. We certainly didn't shy away from trying to get back into the game and having opportunities.
"I was a little bit frustrated we didn't show enough in that first period because, for the amount of possession they had, they never really tested John Ruddy to the degree they would have liked."
Midfielder Wes Hoolahan, a reported target for Aston Villa, remained on the bench throughout but Hughton insisted the player was staying at Norwich.
He said: "There is no situation. He is a Norwich City player. He was very much in my thoughts to play today and is a strong part of my squad."
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