West Ham snapped up Morrison after a troubled time at Manchester United.
"There was a few mooted bigger clubs than ours that wanted him," Allardyce said.
"But that would have been a mistake had he gone there because that might have ended up with him having the same problems that he had at Manchester United. His football is his all, it's all he wants to be and all he wants to do but he wants first team football - that's his mentality.
"Fergie (Sir Alex Ferguson) told me about his talent and that was it - that's enough for me.
"'If you can sort this lad out, Sam, you'll have one of the best players you've ever had' - I don't need anything more than that do I? He was coming down here thinking he would play first-team football straight away but unfortunately he found that a little difficult.
"But in the end, for both of us, it has paid off pretty well. We're finding that we have a big talent on our books which is extremely nice when you're a club in our position."