Postecoglou insists hype will not affect rising teenage star Moore
Making just his second start for the first team on Thursday, the 17-year-old shone in the club's 1-0 home win.
"From minute 45 to 65, I thought we had Neymar on the left wing! He was brilliant," Tottenham midfielder James Maddison told TNT Sports.
Postecoglou, whose team travel to struggling Crystal Palace on Sunday, was asked for his reaction to Maddison's comment at his pre-match press conference on Friday.
"We all understand with young players we do have to be really careful, but as I said after the game I don't get the sense that will affect Mikey at all and there's no denying he was great last night... it's exciting for us" he said.
The Spurs boss said he would consider handing Moore his full Premier League debut at Palace, with captain Son Heung-min "unlikely" to feature due to an injury.
"He (Moore) is ready to start any game but I just feel and especially with young players you need to be really careful with their introduction into senior football," said Postecoglou.
"Even last year, he didn't really have a full season of football, he had quite a few injuries."
It could be a straight shoot-out between Moore and Timo Werner for the left-wing spot despite a difficult period in front of goal for the Germany international.
After Werner was replaced at half-time against AZ, Moore moved from the right wing into his favoured spot on the left and went on several mazy runs.
However, Postecoglou expects the Spurs academy graduate to keep his feet on the ground.
"I think Mikey just wants to be Mikey and like I said after the game, what I see with him is that he's very mature for a 17-year-old, he handles things really well," said Postecoglou.
"It's exciting because it filters through the whole club and everyone in the academy will take enormous pride in that. The whole club feels good about seeing someone come through the programme.
"As a manager, you are excited that at 17 you have a player who is showing maturity and a mindset where he is giving himself every chance to be the best player he can be.
"Sometimes young players are exciting but you can see pitfalls down the road, but I don't see that with him. At 17, you think what is he going to be like at 21 and hopefully I am the manager then."
Tottenham are seventh in the Premier League table after three wins in their past four games while Palace, winless this season, are in the relegation zone.