Gareth Barry, who is on a season-long loan from Manchester City, made the breakthrough midway through the first-half with a stunning long-range effort at Goodison Park.
I couldn’t be happier the way we had a clean sheet
Romelu Lukaku spurned several chances to scored his 10th Premier League goal of the season but the Belgian did create compatriot Kevin Mirallas’s 59th-minute strike.
“It was an entertaining game and important to score that second goal,” Martinez told BBC Sport.
“Overall we created a lot of chances, maybe that clinical touch in the final third was missing but I couldn’t be happier the way we had a clean sheet. Some of the phases of our game were fantastic.”
Meanwhile Norwich boss Chris Hughton rued Gary Hooper’s first-half miss which came before Barry’s opener on Merseyside.
“They were good. We knew that before we came here, there isn’t a side who has come here and had more possession this season,” Hughton said.
“What you need to do is stick in there. We had the best chance of the half through Gary Hooper, they score a spectacular goal.
“In the second half I thought we gave a good account of ourselves but we were up against a really good unit.”
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