The Spaniard was frustrated as his side outplayed the Hammers for spells, but they conceded two relatively soft goals.
The first, from Matt Jarvis, was a cross that went across the goal and inside the far post, before Kevin Nolan added a second to ensure the three Barclays Premier League points.
Wigan could not capitalise on their own possession and pressure, despite the best efforts of the outstanding Shaun Maloney, leaving Martinez confused.
"We are disappointed we couldn't get any points because we are getting into the critical point of the season," the Spaniard said.
"We were very soft in terms of keeping that clean sheet. We know what West Ham can do and the goalscoring ability they have and I don't think we were strong enough.
"I enjoyed the second-half performance. I thought that was a dominant as you would see an away team. I won't be able to explain how we lost the game.
"There is no margin of error. We have five games and we need probably three wins. That is something we can achieve.
"We were the better team. We need to address not conceding cheap goals but in every other department we were the better team."