Spurs moved five points clear at the summit after they recovered from a sluggish first half at Selhurst Park to score twice in 13 second-half minutes.
An own-goal from Joel Ward broke the deadlock in the 53rd minute when he deflected James Maddison's cross beyond Palace goalkeeper Sam Johnstone and it was 2-0 soon after when Tottenham captain Son Heung-min steered home after Brennan Johnson's assist.
Jordan Ayew reduced the deficit for Palace in the fourth minute of stoppage-time, but Spurs held on to extend their unbeaten top-flight run to 10 matches and move five clear of Manchester City and Arsenal, who play Manchester United and Sheffield United respectively across the weekend.
"Let them dream. That's what being a football supporter is all about. It's fair to say this lot have suffered a fair bit, so I'm certainly not going to dampen that," Postecoglou said.
"Top of the table is great and the results are great but it's more in the manner we're doing it. Pretty much from the first game we've had all sorts of different challenges we've had to overcome.
"Every time there has been a real focus and clear-headedness about the group collectively to deal with that.
"That has been a really pleasing thing and because they're getting rewards from that, then that gives us the opportunity to accelerate the growth of giving them more tools out there to help them for whatever we need to overcome."
After returning to the Premier League summit with a 2-0 win over Fulham on Monday, Spurs struggled in the first half at Selhurst Park before working it out in the second stanza.
"I have always felt that matchdays are about the players. What we try to do on a daily basis is give them the tools to find the solutions," said Postecoglou.
"We prep them for their exam at the weekend, but we don't know what the questions are going to be. They've got to work them out themselves.
"In an exam you are not asking anybody for help. You have to work it out yourself and hopefully what we've given them is the tools."
