Byram avoided surgery to resolve a hip injury during the summer and made his first appearance of the season when starting in Leeds' 2-1 Championship home defeat to Burnley.
The 20-year-old right-back made his return to senior action after a five-month absence, but was withdrawn during the second half.
"It was a difficult game for Sam," McDermott said. "You're asking an awful lot, he's not played for such a long time.
"He was struggling a little bit at half-time, so he got to 60 minutes and we took him off."
When asked if Byram was struggling with his match fitness or troublesome hip, McDermott replied: "I don't know, we'll have to wait and see. He's a little bit sore.
"We're just hopeful that he's going to come through and get stronger for that 60 minutes."
Leeds went down to back-to-back defeats last week - at Reading and against Burnley - and McDermott said he is considering strengthening his squad.
"I'd look at the loan market, we'll see," he added. "We got a bit of width on there in the second half (against Burnley) and Dominic (Poleon) was a bit of a threat, but you just have to find a way to get a result and that's all we're trying to do at the moment."