Gareth Barry and Kevin Mirallas struck either side of half-time as the Toffees lifted themselves back into the top four of the Barclays Premier League with a dominant display.
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 a 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."