The Latics' 1-0 victory over United in April was one of the more surprising results of the season and played a key part in their survival.
It is the only one of the 16 meetings between the sides that United have not won, and normal service was resumed earlier this season when Sir Alex Ferguson's side were 4-0 winners at Old Trafford.
Martinez believes the club's perilous situation made them forget about who they were playing that day at the DW Stadium and, although Saturday's victory over Aston Villa lifted them out of the bottom three, he hopes they can adopt the same approach.
The Spaniard said: "United is one of the hardest games that you're going to have in this league. They've set the pace in this year's competition, they've got seven points difference already to the champions, which is an incredible start.
"In the same way, we are in such a situation where we need points that we can't afford to look at who we're playing against. We're playing at home and we need to make sure we take advantage of that.
"If you're looking at the previous games against Manchester United, the last one (at home) is the clear picture we've got in the back of our minds that if we are perfect and perform in the manner that we can do then we can challenge for three points against Manchester United.
"I think it was the first time we played the game without thinking who we were playing against. We were in such a desperate need of points that we could only focus on ourselves and we did that.
"Obviously looking at the rest of the history, the stats are very bleak because it shows you we're playing one of the best teams in the world.
"But we're excited, we're looking forward to it. The result and performance against Aston Villa has given us a real sense of confidence in ourselves and this is an opportunity to show what we can do."
Saturday's 3-0 victory ended a run of only one point from six games for Wigan, and there was more good news for the club today when they announced their financial results for the year to May 2012.
The club made a profit for the first time in six years, ending the season with a net profit of £4.3million compared to a net loss of £7.2million for the previous 12 months.
The news will enable Wigan to press on with plans to redevelop their academy and training facilities, a project Martinez hopes will be completed in just over a year.
He said: "In 1999, moving to the new stadium gave the football club a different angle of what we wanted to achieve.
"Now is a very similar year in terms of investing in the structure and the facilities that will give us a massive boost to become a football club that is close to reaching our long-term ambitions.
"It's an exciting project. We're working already with the architect and our timescale will be trying to complete everything over the next 13-14 months."
Wigan have been battling an injury crisis over the past few weeks but the situation seems to be easing and Martinez has no fresh worries ahead of tomorrow's match.
Midfielders Ben Watson (broken leg), Albert Crusat (knee) and Ryo Miyaichi (ankle) and defender Adrian Lopez (hamstring) are all still out but defender Antolin Alcaraz may be available for the FA Cup clash with Bournemouth on Saturday after recovering from a long-term groin problem.
The Wigan boss may have two new players available by then, with midfielder Roger Espinoza and striker Angelo Henriquez expected to officially arrive at the club this week.
The Latics confirmed the signing of Espinoza from Sporting Kansas City earlier this month and are just waiting for the Honduras international to obtain a visa while Henriquez will join on loan from Manchester United for the rest of the season.
Tomorrow's match could be the last for striker Arouna Kone, though, before he joins up with Ivory Coast for the African Nations Cup.
If the Elephants do well, Kone could be missing for more than a month, and Martinez said: "You don't want to lose players.
"I think this tournament is very unfair on players. It's a magnificent tournament but the timing of it couldn't be worse."
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