Andre Villas-Boas suffered the biggest home defeat of his reign as Tottenham manager on Sunday evening as West Ham ran riot, claiming a fine 3-0 victory in north London thanks to three goals in 13 second-half minutes.
Ricardo Vaz Te doubled West Ham's lead after Winston Reid's opener and Morrison then brought the away fans to their feet with a fantastic solo goal.
West Ham had struggled without the injured Andy Carroll so far this season, but Morrison performed admirably up front, much to Allardyce's delight.
"That was a genius goal," the West Ham boss said.
"Tottenham had conceded two goals before this, but he just headed directly to Vertonghen and Dawson, slipped them like they weren't there and he used his outstanding ability to dink the goalkeeper.
"For me you will struggle to see a better goal this season."
Many questioned Allardyce's decision to sign Morrison from United last year.
The midfielder was convicted of two counts of witness intimidation and he was also fined B£7,000 by the Football Association for a homophobic tweet.
The player failed to settle originally at West Ham and was loaned out to Birmingham last season.
But 12 months on, Allardyce says the 20-year-old is a changed man.
"The penny has dropped with him," Allardyce added.
"It has dropped in lifestyle and attitude and his timekeeping, all of a sudden there is a belief that he doesn't want to do anything other than break into our first team.
"I think that 12-month spell at Birmingham gave him a time to reflect on what it takes to be a player on a week in and out basis."
Allardyce revealed that former United boss and close friend Sir Alex Ferguson told him he was getting a potential star when he signed Morrison in a deal that was reported to cost the London club just B£1million.
The West Ham boss said: "When I signed him Sir Alex said 'I hope you can sort him out because if you can he will be a genius'.
"He needed to get away from Manchester and start a new life and it looks like it is paying off for us.
"The fans at Tottenham thought it was going to be a nice easy breeze, a nice comfortable three points.
"But the Premier League will tell you that if you think like that you are going to get your backside kicked and they got their backside kicked."