Everton looked to be on the way to a win that would have moved them into the top four of the Premier League when Kevin Mirallas put the visitors in front four minutes before the interval.
But their hopes were dashed in the 75th minute as West Brom defender Diego Lugano headed home the first Premier League goal of his career to earn a point for new head coach Pepe Mel in his first game in charge.
The draw keeps Everton a point adrift of city rivals Liverpool in fourth ahead of the Merseyside derby next Tuesday.
And Martinez was quick to express his dissatisfaction with his side for failing to kill the game off.
"Any point is a good point," the Everton manager told Sky Sports. "(But) we are disappointed with the second-half performance.
"The hardest thing in first half was to get the goal and we managed that.
"The second half I must admit the condition of the pitch didn't allow us to control the game in the way we wanted, to concede the goal in the manner that we did was unfortunate."
Midfielder Gareth Barry feels Everton will be in the mix for a place in the UEFA Champions League if Martinez's men maintain the strong from they produced earlier in the campaign.
"It was a fair result in the end," Barry said. "It's nine draws for us now and that's too many. But if we show the form that we showed at start of season then we'll be there or thereabouts."
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