An injury in the warm-up to Joe Dudgeon meant Doncaster-born Holgate, a second-year in the Under 18s, was called up to feature at right-back having originally been named as a substitute to face his hometown club Rovers.
"It's really pleasing for all of the Academy staff to see Mason make his debut," Branson told barnsleyfc.co.uk.
"I think he played well. He played right-back which is slightly out of position. Mason is more of a centre-half but it's difficult sometimes to put a young lad straight in at centre-half.
"He does the centre-half side of things well - by organising, clearing the ball and heading it but he also has a composure and calmness that most centre-halves haven't got. He can play out from the back and put balls in behind people. He's got a calmness about him which we really like and he doesn't flap or panic.
"We were pleased with his performance but, more importantly, Danny (Wilson - Reds Manager) was pleased as well."
Holgate is the fourth Academy player to make his full debut this year, following on from James Bree, Rhys Oates and Brad Abbott - with the latter also coming on as a substitute against Doncaster.
"It's great to see Brad (Abbott) in and around the first team again too. He's been patient in the Under 21s and waiting for the opportunity to come. Things are going okay. We don't rest or sit back because we want the next one to come through. It's a process going right down the Under 13s and even below that."