Martinez's side suffered their third Premier League defeat in a row when they were beaten 3-1 at QPR on Saturday and they have not won a top-flight fixture since their 2-1 victory at West Brom on December 10.
The result leaves them bottom of the table, four points adrift of safety, and widely tipped to go down, but the Spaniard - who guided the club to survival on the final day of last term - sees things differently.
He told the Wigan Observer: "I don't think the situation at the moment is any different from the ones we've faced in the past.
"If you listen to anyone outside Wigan, I don't think many of them have really high hopes for us.
"But I think that's probably the biggest strength we've got - that siege mentality - and we need to take advantage of that.
"We know what we have to do and we know how we are going to achieve it.
"It's just a matter of working as hard as we can to maintain our standards.
"It's always nice to have that added motivation to achieve, and it makes it sweeter when you do it.
"This club has always defied the odds and we're determined to make sure we do it again this season."
Martinez looks set to soon inject some fresh blood into his team's bid to beat the drop.
Bristol City have given Wigan permission to open talks with Nicky Maynard, with the two clubs close to agreeing a fee for the striker.
Maynard, 25, had been made available for transfer by the Robins after ending talks over a possible new contract and a brief statement on City's website read: "Discussions to finalise a transfer fee with the Premier League club are at an advanced stage."
The Latics are also understood to have agreed an undisclosed fee for Birmingham's 27-year-old Chile winger Jean Beausejour.
Meanwhile, Wigan forward Hugo Rodallega, who is out of contract in the summer, has reportedly told a radio station in his native Colombia that he will not be staying at the DW Stadium beyond the end of his current deal.
Rodallega, 26, joined the Latics from Mexican club Necaxa for £4.5million in 2009.
He has gone on to become Wigan's record goalscorer in the Premier League, netting 24 times, but his strike in the QPR game last weekend was only his second of the 2011-12 campaign and he has struggled to hold his place this season.
