Spurs were 2-1 up heading into added time at the Tottenham Hotspur Stadium but veteran defender Mats Hummels snatched a late equaliser for Claudio Ranieri's team.
It came just days after Spurs hammered Premier League champions Manchester City 4-0 at the Etihad.
Spurs are sixth in the English top flight ahead of Sunday's match against mid-table Fulham, with six wins and five defeats so far this season.
Australian coach Postecoglou said he would stick to his attacking principles despite his team's slip-ups.
"There's plenty of room for pragmatism in all walks of life and in football as well," he said at his pre-match press conference. "But I'm just not interested in it.
"I don't know why I need to change my approach to be like everyone else wants me to be. I'll continue to push this team to be a little bit different, play football in a different way.
"Maybe when I'm long gone you'll all pine for my entertainment, and you'll have had your fill of pragmatism.
"But look, if we were pragmatic I'd say at 2-0 up at City away, we'd have probably settled for 2-0 and we wouldn't have got the victory we did and made it a special moment for our club."
Postecoglou said his approach was geared towards long-term success for the club, who have not won silverware since 2008.
"At the moment what do we have? We don't have a hell of a lot," he said. "We haven't achieved anything yet, we haven't had success, we haven't done all those things we want to do.
"So if I start being pragmatic now then maybe we'll never get there. Last night we weren't at our highest level but I thought for 20 minutes we were as exciting as we've been since I've been here... we were exciting to watch. And that's what I want."
He hinted at potential signings in the January transfer window, saying he had spoken with technical director Johan Lange.
"Last year, we ended up doing a little bit of business which I think helped us but nothing is concrete now because January is always tricky and a lot will be dependent on where we are squad-wise," he said.
