The Latics became the first side to win at Turf Moor this season after their 3-1 success but the victory came at a price.
Defender Maynor Figueroa, Paul Scharner and Hendry Thomas all picked up knocks against the Clarets but, while Scharner and Thomas were able to play on, Figueroa was forced off after just 28 minutes with a medial ligament injury.
The defender faces a number of weeks on the sidelines but Martinez highlighted that the Honduran was keen to play on, as was Scharner, despite needing 10 stitches to an eye wound he picked up prior to Wigan's third goal.
Chris Kirkland was another who was desperate to play despite dislocating his little finger last week against Manchester City and Martinez was delighted with the squad's attitude.
"Maynor has a grade two medial ligament problem in his left knee," he told the Wigan Evening Post.
"We will assess it further to see how bad he is, but it doesn't look too good. Normally with this sort of injury, you are talking about weeks rather than months - but the signs are not nice.
Serious injury"He actually wanted to carry on, but the injury was serious and he couldn't do so. It's not an injury that he would have damaged any further as it was just a tear - it's muscle problems that can get worse - but Maynor felt so uncomfortable that he had to come off.
"Paul and Chris both played through the pain barrier, while Hendry Thomas took a nasty knock in the face from the ball in the second half which affected his vision.
"It shows you the character that is in the squad and, when you have that attitude - when your team will do anything to win a game - it's something to be proud of.
"Paul battled on to make a difference and now has 10 stitches above his eye to worry about, but there were no reactions to any of the existing injuries."