The 18-year-old defender made his senior debut during a 1-1 draw with Aldershot last weekend and is hoping for more opportunities to impress in League Two.
"It was good to make my debut and get that out the way," said the Northern Irishman. "I obviously want to spend more time on the pitch but I will respect the manager's choices and give it my all whenever given the chance.
"I did okay for my debut. There were one or two sloppy passes but, all in all, I think I did quite well.
"I have only been here for a very short time but have already learnt so much just by being here and I just want to keep learning whilst giving it my all when given the opportunities."
Warren Joyce commented to ManUtd.com on McCullough's current situation: "Luke’s made his debut for Cheltenham and they are near the top of the league.
"He’s got to fight to get into a team going for promotion and he gave a good account of himself when he came on at the weekend. It’s up to him but hopefully he’ll be involved this Saturday again."