Hammers manager Allardyce handed Morrison his full debut against League Two Cheltenham and the 20-year-old former Manchester United starlet marked it with a stunning goal as the hosts eased into round three with a 2-1 victory.
"He's not bad, is he?" said assistant boss Neil 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.
Collecting the ball on the edge of the area just 40 seconds into the second half, Morrison turned inside, then out, leaving the entire Cheltenham defence wrong-footed before curling the ball low into the corner.
"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."
West Ham were already leading through Ricardo Vaz Te's curling free-kick, awarded after Morrison - who moments earlier was booked for diving - had been fouled 25 yards out.
The Hammers should have been home and hosed long before Cheltenham got back into the match.
Substitute Stewart Downing came agonisingly close to his first Hammers goal but his header flew inches wide while Vaz Te was denied by a fine save from Scott Brown.
But Town pulled one back in bizarre circumstances in the 57th minute when Spanish goalkeeper Adrian, making his debut, got in a horrible mix-up with James Tomkins and was penalised for a foul on Jermaine McGlashan.
Matt Richards stepped up to tuck in the spot-kick, and it should have been game on.
But the visitors rarely threatened an equaliser - a Ryan Iniss header which flew wide was as close as they came - while West Ham should have enjoyed a far more comfortable night but Jack Collison's drive was tipped over, George McCartney's header hit the crossbar and Taylor's late shot was cleared off the line.
Cheltenham boss Mark Yates 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 revealed.
"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."