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Spurs are 10th in the Premier League after an inconsistent campaign and, although Postecoglou has been criticised for his team's tactics this season, he recently said "in tough times you double down on your principles".
Slot was heavily linked with taking over as Tottenham manager in 2023 before staying at Feyenoord, and takes his side to play the London club on Sunday (16:30 GMT).
Liverpool have also been drawn against Spurs in the semi-finals of the Carabao Cup, with Tottenham progressing after a rollercoaster 4-3 win against Manchester United.
"It's great work that Ange is doing. I hope, hope, hope that he (Postecoglou) wins a trophy - not the League Cup but I am completely a fan of his team for the Europa League," said Slot.
"People talk about trophies, trophies, trophies and that is so important. For me, his brand of football is so much more important.
"If he can combine it with winning something that would be so good for football in general because then people can stop talking about 'is it too attacking?' How on earth can you play too much attacking football?"
Slot added: "I think it is a privilege to be a season ticket holder at Tottenham and to be a fan of them at the moment because they play such a great style."
Tottenham are the second highest goal scorers in the Premier League this season with 36 - just one behind Chelsea - having won seven and lost seven of their 16 top-flight games.
"I really have to give them credit," said Slot. "They have always been a certain brand of football for me and a certain identity and Ange Postecoglou gives them that identity back completely.
"Every time, it is a joy to watch them. Once in a while results go against them but I think they are one of the teams to beat Manchester City like us."
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