Marouane Fellaini went the closest to scoring as he struck the post late on, with the Blues creating the better chances of a tight Barclays Premier League contest at Goodison Park.
A Seamus Coleman cross-cum-shot also rattled the woodwork as the game entered injury time but the Baggies held on for a point in a lively finish.
Martinez said: "We knew it was going to be a really tough game. It was a really hard-fought game for both teams.
"West Brom came with intent to keep a clean sheet.
"I was very happy with what we did off the ball. We suffocated West Brom and Tim Howard only had a couple of saves.
"It was just getting that goal. I think we did enough to get the three points but the ball was bouncing in and bouncing out, that was the difference."
- Sports & Recreation
- Barclays Premier League
- Seamus Coleman
- Marouane Fellaini
- the Baggies