The Latics dominated proceedings at the DW Stadium but could only manage a 1-1 draw, with Wigan old boy Paul Scharner cancelling out James McArthur's goal.
The point lifted Martinez's side level on points with QPR and Wolves at the bottom but they have played a game more than their rivals and have matches against Liverpool, Chelsea, Manchester United and Arsenal to come in the next month.
The Wigan boss said: "It's a really frustrating feeling and you feel it is a football injustice but today I really enjoyed the performance.
"At the moment it is not going our way. To finish that first half 0-0 was tough to take but in the second half we started on the front foot, we earned the goal and then just that feeling of having something to lose, they had two corners and they scored.
"We need a scrappy win to build a little bit of confidence and belief. In football terms it is impossible to explain with that performance how we didn't end up with three points.
"I'm really proud of the players because if we carry on playing like that lady luck will come to the DW Stadium.
"I feel this squad is too strong not to carry on performing in that manner and if we do we'll get the points, I've got no doubts about that."
Wigan dominated from the off, with Franco Di Santo firing in three shots in as many minutes, the last of which forced Ben Foster to tip over the bar.
Time and again the Latics threatened Foster's goal, twice hitting the bar in the first half through an Emmerson Boyce header and James McCarthy's 20-yard effort, but the ball would not go over the line.
They were finally rewarded nine minutes after the break when Victor Moses caused havoc in the West Brom defence, cutting in from the right and McArthur poked in his third of the season.
It was thoroughly deserved but in the 65th minute they switched off from a corner, allowing Scharner a free header, and they could not find a second despite a late flurry of chances.
West Brom boss Roy Hodgson was happy to admit his side were second-best but praised the players for their attitude.
"Wigan played very well," he said.
"It was obviously a very important game for them to win and they certainly went about it in the right way, they committed a lot of players forward.
"I don't think we were anywhere near our best in terms of our attacking play but I left a few players out of the team to give others a chance. I've got to be very satisfied with a point and sympathise with Wigan, while praising my team for their resilience, for their character and their desire to get something out of this game despite the fact we're in a more comfortable position in the league.
"We could have been expected on a day like today to crumble and succumb to the pressure but we never did."
Hodgson, meanwhile, felt referee Michael Oliver was right to keep his red card in his pocket after a second-half melee sparked by Youssouf Mulumbu's reaction to a tackle from McArthur.
Mulumbu, Jerome Thomas and Boyce were all booked, and Hodgson said: "He (Mulumbu) pushed him but it was one of those things you're going to see quite often in a game.
"I didn't think there was anything particularly vicious about it and it would have been a bit sad if any players had been sent off for that. It was a bit of a storm in a teacup.
"Youssouf felt he'd been kicked as he was stumbling and reacted, it was human nature. I was pleased the referee showed common sense."