Young midfielder Davies came off the bench for injured Oyvind Leonhardsen after 15 minutes and grabbed his chance with two superb finishes for his first two goals for Spurs.
Boss George insisted: "Simon is good at going forward and a good finisher.
"There are still aspects of the game that he has to learn but he has two good feet and in training he is one of the best finishers at the club, so when he breaks from midfield you know he will nearly always hit the target.
"He got his chance and that's football. Somebody gets an opportunity and the young boy seized his today.
"You dream of these things and that's why it's a game that we love."
Ledley King settled any early nerves with the opening goal, Davies struck the second and Luke Young's cross was turned into by a defender for 3-0 before the break. Davies hit his second and our fourth just four minutes into the second half and that was that.
"I was very pleased," added George. "Considering the injuries we picked up again in the week and the fact we had players playing out if position again, I thought it was good. I' m delighted - 4-0 and we're in the quarter-finals.
"We have laid a base defensively over the last few weeks and now we are starting to work in midfield and attack. Ledley King and Luke Young were outstanding again. There were some good performances out there.
"Stockport were a very hard-working team that gave us little time to relax. It was a very well-contested game."
As for 'Leo', George revealed that it was an ankle problem and the club would have to wait for the results of tests to determine the extent of the damage.
Listen to George's post-match press conference in full by clicking here
George Graham was full of praise for two-goal hero Simon Davies after Saturday's convincing passage into the FA Cup quarter-finals.