Stam had only just been introduced as a second-half substitute when he went down after a heavy tackle. The Dutchman was unable to return as Wigan slipped dangerously close to relegation, and it is evident he will now miss Saturday's FA Cup Final, plus Wigan's final two Barclays Premier League games.
"We will check Ronnie tomorrow, but it seems it is a broken leg," said Martinez. "He couldn't put any weight on it, so he will need a scan tomorrow to find out exactly what it is."
It capped a disastrous night for Wigan, with Martinez also confirming the hamstring strain that kept Jean Beausejour out of the game is also virtually certain to end his season.
"Jean has a tear in his right leg," said Martinez. "It will be difficult for him to be back before the season ends."
It completed an awful evening for Wigan, who are now three points from safety, with only two games remaining - including a trip to Arsenal - and their run-in complicated by Saturday's FA Cup final.
The manner of the defeat was even more shocking given Wigan had twice led, through Roger Espinoza and James McCarthy, only to concede awful goals, due directly to defensive mistakes. The Latics were floored by second-half goals from Angel Rangel, Itay Shechter and Dwight Tiendalli.
"We shot ourselves in the foot," said Martinez. "We had an incredible opportunity against a team in mid-table, who had not won for a while. We did not take that chance.
"We had a 10-minute period when we should have been stronger and made better decisions but we could not cope. The dressing room is really down. But we will never throw the towel in.
"It is not a bad thing to feel down but now we need to fight for every single point. We have done it before and we can still do it now. We got a very important victory at Arsenal last year and we need to do it again."