Spurs took an early lead through Dominic Solanke, but lost 2-1 as Anthony Gordon and Alexander Isak struck for the visitors.
Postecoglou later said: "On the balance of play, any balance you want with all things being equal, we would have won today.
"Outstanding. I couldn't be prouder of the players. I couldn't ask any more. It's a game we would have won if all things were equal.
"If all things were equal and balanced we would have won today. Things weren't equal and balanced."
When asked what was not equal, if it was Newcastle's opener: "You can talk about whatever you want. You want my opionion - if all things were equal and balanced we would have won.
"We had plenty of chances. Our football was outstanding considering everything we're going through.
"If it was an even playing field we'd have won."
On keeper Brandon Austin's debut, he added: "Really good. The moments we are going through putting big tasks on players and they're rising to occasion.
"The performance deserved a victory."
Postecoglou also stated: "I'm hugely proud of my players. We were outstanding considering the situation we are in. We deserved to win that game. I don't feel hard done by - that's the way they do things.
"At half-time, full-time, I'm hugely proud of my players.
"We are are disappointed because all things being equal we'd have won. You can only do things that you can control, and there were things there today that were out of or control that took the game away from us."