The Latics began the match hoping to end a five-match losing run and it looked like they were on course for only a fourth victory of the season when, with 14 minutes remaining, Phil Neville deflected Jean Beausejour's cross towards the arms of Tim Howard only for the ball to spin off the turf and into the net.
But Everton substitute Victor Anichebe headed in the equaliser seven minutes later to leave the Latics still five points adrift of safety.
Martinez has frequently bemoaned his side's misfortune this season, and he said: "It was a welcome surprise.
"In the second half we had that little bit of luck. We haven't had much luck this season and in the first half there were a couple of situations where you felt the ball was going to bounce into the striker instead of the centre-half but we didn't get that.
"I thought the break was what we deserved after the dominance we had and the attacking threat we showed, and the real intent to try to play our football in difficult conditions.
"At that time I thought it was the right reward and it looked like it was going to be our day, but unfortunately it wasn't."
The game was thoroughly forgettable until Howard's horror show, with both sides struggling to create chances or find any rhythm on a cold and wet afternoon.
Everton had looked a little flat after their efforts in beating Barclays Premier League leaders Manchester City on Tuesday but they responded well to going behind and were level again soon.
Wigan could only clear a Leighton Baines corner straight back to the full-back and his cross was headed in by Anichebe, who had only been on the field for two minutes.
Although they did not manage to hold on, Martinez felt the display was a real step up from defeats by QPR and Tottenham.
The Spaniard said: "We were never outplayed, we were never opened up, we had a few set-pieces to defend and it was unfortunate in the second phase of a dead-ball situation that they found the net.
"We know Everton do that regularly, it's one of their biggest strengths, but I thought we defended throughout the game really well and I was extremely pleased with the performance.
"Everton were coming into the game on the back of a very good result against the league leaders, full of confidence, and I felt we were the better side and we dominated the game.
"And that pleases me after the last two performances, where we didn't do that for 90 minutes. It's a real positive going forward."
Everton manager David Moyes gave midfielder Steven Pienaar a start after he rejoined the club on loan from Tottenham this week while new striker Nikica Jelavic came on as a second-half substitute.
The Scot felt his side paid for their efforts in beating City and argued Wigan's pitch had to take some of the blame for the goal and the quality of the game.
Moyes said: "I think the effort we put in in midweek, physically and mentally, did take a bit out of us but Wigan had to play as well so it was the same for them.
"We never really sparked. When we went a goal down we came alive and looked as if we were going to get back in it but we were waiting on it happening today [Saturday] rather than making it happen.
"But I didn't think we looked like we were going to concede a goal today [Saturday], we looked comfortable most of the time, and it was a complete freak.
"The pitch here is really heavy and it's going to take its toll. It was hard for them to play on and run through - compared to pitches they play on nowadays. In our day they were the norm."