The Saints had to remove the winger after 38 minutes during their 3-2 Carabao Cup win.
Fraser had been hoping to earn more game time and did try to play on during the game.
"We had a few guys that were going to play tonight that couldn't because they're not very well," Martin explained, speaking to the Daily Echo.
"We've had a bit of a virus and stuff in the camp. I think everyone's had it at various points over the last couple of weeks.
"Flynn and the gang were just not feeling very well. Wee Man was not feeling great before the game but wanted to give it a go. He just felt a bit tight and a bit tired.
"He didn't have the usual spark he normally has, so he came off, but he gave it a go and wanted to give it a go.
"I think that'll be important for him, even having half an hour and hopefully he feels better very quickly.
"Hopefully by Thursday we'll have everyone back training and feeling okay. Jack was on the bench tonight, but maybe would have played if he felt better after Saturday.
"Adam (Lallana) is fine, we're just managing his minutes. We had a couple of guys at the training that were not involved.
"Ryan Manning just ticked over really because he's not been feeling great since the weekend.
"I expect some of them to train tomorrow and most of them, if not all of them, to be ready by Thursday or Friday."