The relegation-threatened side looked on course for three much-needed points when Rodallega needlessly handled a corner.
Wigan manager backs Rodallega after costly handball
The relegation-threatened Wigan looked on course for three much-needed Premier League points at the DW Stadium when Rodallega needlessly handled a corner.
That allowed former Wigan defender Leighton Baines the opportunity to step up and smash an equaliser from the spot after 77 minutes.
Wigan had led courtesy of a fine strike by Charles N'Zogbia in the 21st minute and had already survived one penalty scare when Ali al Habsi saved from Mikel Arteta.
"Hugo is devastated, as you can imagine," Martinez said. "Those are incidents that happen. Prior to that he had made three great actions at corners, defending with great aggression.
"Hugo has won so many points for us and will carry on winning points for us.
"That is the nature of the game and we will support him."
The strike by Baines prevented Wigan from climbing out of the relegation zone and moving two points clear of Blackpool.
The home side finished strongly but found Tim Howard in fine form in a frantic closing period, the American goalkeeper producing four good saves.
Wigan now have just three matches to save their top-flight status, including one crucial encounter with fell stragglers West Ham United in two weeks.
Added Martinez: "It is disappointing because we couldn't get the three points but we knew it was going to be a very difficult game.
"Everton showed the experience they have got and what a competitive side they are. I see it as another point. I don't think we could afford to lose today.
"Unfortunately, this is going to take the fight to the last week of the season but I think that is what we expected.
"It is a real fight, a real challenge. We have got three games to go and I feel we are capable of getting points against anyone.
"I saw great character and great bravery today.
"We see it as a phenomenal challenge. Everyone expected Wigan to go down and we are really excited to try to defy the odds."
Steve Round, the Everton assistant manager, conceded that the visitors had found the going tough.
Said Round: "It was a struggle. We were playing against a team that are fighting for their lives.
"Unfortunately, we missed a couple of chances and missed a penalty and we thought it was going to be one of those days. But credit to the lads, they showed great resolve and resilience, as Everton do."