The north London side were denied at the death when Mats Hummels snatched an equaliser for Claudio Ranieri's men.
Goals from Heung-min Son and Brennan Johnson had cancelled out Evan Ndicka's leveller for the visitors in arguably the most anticipated clash of this week's Europa League fixtures.
The result leaves Spurs in ninth and one place outside of the automatic qualification spots for the round-of-16 stage.
Postecoglou expressed his frustration that his side were unable to see the game out after finding themselves in a commanding position.
In his post-match press conference, the Spurs boss was asked whether the remaining three games would see his side prioritising winning over style of play.
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However, the Australian was unanimous in his response claiming that his philosophy will always include entertaining the fans.
"No," Postecoglou said when asked if he would switch up his approach, leading to laughter from those present. "Why can't it just be entertaining, mate?"
He continued: "Isn't that why we all come? Would you really prefer us to sketch out a couple of 0-0 draws and a 1-0 win and we get through?
"I'd much rather we were exciting to watch and it's edge of the seat stuff. Sometimes you don't get the reward we could have tonight.
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"I'd like to think when you tune in to us, you get entertained."
With key games against Rangers, Hoffenheim and Elfsborg still to play, Postecoglou knows his side have their destiny in their own hands if they are to avoid February's play-off round.
After a blistering start to their Europa League campaign with three-consecutive victories, Spurs have taken just one point from their two games against Galatasaray and Roma, conceding five goals in the process.
Tottenham's swashbuckling style has made for entertaining viewing but defensive frailties are all-too often exposed.
With key games against Rangers, Hoffenheim and Elfsborg still to play, Postecoglou knows his side have their destiny in their own hands if they are to avoid February's play-off round.
That said, former Spurs boss Harry Redknapp doesn't see the club changing their style anytime soon due to the players at Postecoglou's disposal.
"That's the type of player he's got in the team, they're not set up to defend," Redknapp told talkSPORT Breakfast.
"Full-backs love to go forward and the midfield is pretty open, that's how they play.
"They've had a couple of results where you certainly would have expected them to win, but they're still only a few points behind Arsenal and a couple behind Man City."
"They're going okay," Redknapp added. "Last night's game was a difficult game. It's a league table where it's not do or die.
"There's always tomorrow, get a result in the next game or the game after. So I wouldn't take too much out of last night. The last game for me was obviously the Man City game. It was a fantastic performance.
"They can build on that at the weekend against Fulham, which won't be easy. Fulham, on their day, can give anybody a stiff test. But it'll be interesting. And don't forget they lost to Ipswich."
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