McAllister was delighted with the 18-year-old midfielder, who signed a four-year contract just 24 hours earlier and scored the first of his side's goals as Leeds chalked up their first home league win of the season.
McAllister said: "He is very pleasing on the eye and a very good footballer.
"We have to add little pieces to his game. We don't have to tell him much about how to control the ball or how to pass it. He has that in abundance.
"He plays in the area of midfield where I played so it is an area of the pitch I naturally look at a lot.
"I asked Fabian if he could take another step forward by having a pop at goal. He cracked one in in this game and I was very pleased."
Leeds moved into the League One play-off zone thanks to the win and McAllister admitted that the result had defused pressure around Elland Road.
"I know its only four games in but you look at league tables and it doesn't quite reflect where your form is," he said. "We needed a result, there was a wee bit of pressure leading up to this game.
"We got an absolutely perfect performance for 90 minutes. Barring the last two minutes (of stoppage time), every player and each of the substitutes were first class."
Goals from Delph, Alan Sheehan, Jonathan Douglas, Jermaine Beckford and substitute Andy Robinson turned the game into a rout before a late lapse in concentration enabled Crewe to score twice and regain lost pride.
Beckford's apart – which was still a good near post header – all would easily have been contenders for any Goal of the Month competition.
Delph, Sheehan, and Douglas struck from long range while Robinson curled the ball into the top corner from the edge of the penalty box.
Substitute Robinson had also struck the bar and provided the cross for Beckford's goal.
Defender Lubomir Michalik faces a suspension after being sent off in stoppage time for pulling the shirt of Crewe substitute Clayton Donaldson.
His misdemeanour resulted in Crewe's first goal from the subsequent freekick and was quickly followed by a second scored by Eugen Bopp.