Morrison was given his full debut for West Ham in the second-round tie and scored what proved to be the winner in a 2-1 success at Upton Park.
The former Manchester United youngster had caught the eye in pre-season and McDonald acknowledged the 20-year-old is now pushing for a regular first-team role.
"He's not bad, is he?" said McDonald. "He scored some good goals in pre-season and he's had to be patient, but he's come out and showed what he is about.
"He showed composure, he's knocked on the door and that's what the manager wants. He adds to the competition for places that we want on the pitch."
Morrison was once tipped as the finest talent to come out of the Old Trafford Academy since Paul Scholes, but he left 18 months ago amid rumours of ill-discipline and a poor attitude.
However, a season on loan at Birmingham appears to have done him the world of good and, while he has a long way to go to live up to the hype, Morrison offered a tantalising glimpse of his potential.
"As a young kid coming from Manchester thinking he could walk into the team, it was a bit of a shock to him that he didn't," added McDonald.
"I think the penny has dropped now and he's come back a wiser young man and we look forward to him keep knocking on the manager's door.
"Now he has to keep scoring, he has to keep the ball, his all-round performance has to be good and he has to be consistent."
Cheltenham boss Mark Yates, whose side pulled a goal back from the penalty spot through Matt Richards, revealed he was well aware of the threat posed by Morrison.
"I'd seen him at Birmingham and only today his agent was telling me what a good player he is," he said.
"We could have done better with that goal but we showed our character - we could have capitulated after that but we didn't and we gave ourselves a chance in the last 15 minutes.
"We rode our luck at times to even still be in it but we had a couple of chances and we showed we have a bit about us.
"But West Ham are a really good side, they've got quality players."