The Latics had gone six Barclays Premier League games without a victory before their 2-1 win against the Hammers, which gave them breathing space over the bottom three.
But, more importantly for Martinez, it was also just reward for their performance, something he felt had been sorely lacking this campaign.
He said: "It was a key moment in our season and now we need to show that consistency in the weeks ahead. People had started to look at the table and get a bit anxious.
"In football you play to win games and win points and when you get into a little bit of a negative run in terms of points, even though the performances are good, you don't want to create a problem when there isn't one.
"That game was probably the moment we had to win to get away from those thoughts. The way we had to perform, I've seen it time after time, you're so desperate to win you forget how you're going to win and it becomes a big mountain.
"And it was the complete opposite. Now is the moment to carry on that level of performance."
Wigan won their first away game of the season at Southampton but since then have failed to pick up a point on the road, losing at Manchester United, Sunderland and Swansea.
White Hart Lane has not always been the best venue for Wigan, notably when they were beaten 9-1 in November 2009, but they bounced back the next season with a 1-0 victory, their first win at the ground.
Martinez said: "We've been mentally very strong to cope with the previous results that we had at White Hart Lane.
"I think we're well over that, now it's more a case of being able to produce the level of football we've had at home away from home for the duration of the 90 minutes.
"Our performance at Southampton was a very good performance. We need to learn a little bit from the last two performances against Sunderland and Swansea, and there are many things we need to get right.
"Spurs will test us to the limit and it will be a fantastic challenge for us to see how we've addressed those problems."
Tottenham had a slow start to the season under new manager Andre Villas-Boas but have since picked up extremely well, winning five of their past six games in the league, including away at Manchester United.
Martinez believes there is plenty more to come from Spurs and would not be surprised to see them involved in the title race come the end of the season.
He said: "I do feel this team is capable of anything this season.
"We saw them going to Old Trafford and getting a very important win, and that wasn't a surprise really given the quality they've got.
"Spurs haven't reached their true potential yet. I think the new manager has come in and is slowly putting his own stamp on things but in the wide areas they are world class, the new additions are world class with the likes of Mousa Dembele and Clint Dempsey.
"White Hart Lane brings a real good football tradition and a great glamorous occasion and probably that's the hardest thing we need to deal with, to go there and be ourselves.
"We know what level we need to be at to get a positive result and that's what we'll look for."