The 20-year-old was sold by Manchester United boss Sir Alex Ferguson, who admitted at the time that he had lost patience with the youngster over a number of off-pitch issues.
He has since become a key part of the West Ham starting lineup this season, as well as breaking into the England Under-21 side, but Allardyce has conceded that the attacking midfielder initially struggled to adapt at Upton Park.
"Certainly, we had early problems with him and his self-discipline and self-organisation. He just wasn't functioning properly. He was always late, his diet was bad," Allardyce told the Daily Mail. "There was a time when I wondered if maybe it wouldn't work, that I couldn't do it with him.
"The problem was that he thought he was coming here to play in the first team. Then he wasn't in the team and he wasn't interested. Players like Kevin Nolan and Mark Noble actually told him, 'You have no chance'. He didn't take it well. He had been told so many times that he was so good that he thought he could breeze it.
"Really gifted young players can lack the desire, edge and dedication and that was Rav. It's a player's brain that makes him a top player. So we got him a loan at Birmingham and they had the same problem until they had injuries and he got in the team and stayed in."
Morrison is expected to be part of the West Ham team that will take on Manchester City this afternoon.