Moyes's side reduced the gap on the table-topping Gunners to five points after a stuttering start to the season.
However, despite the win against Arsene Wenger's side, Lawrenson feels that United are still unlikely to retain their Premier League title.
"They are still a work in progress," Lawrenson told The Mirror.
"There is still so much for David Moyes to address with the champions and the points dropped already will cost them.
"Arsenal are still the team to catch."
United are currently on a nine-game unbeaten run in all competitions.