Spurs meet Manchester United in Bilbao sitting one place outside the bottom three.
But Gazza told Tribalfootball.com: "I think so (Postecoglou should keep his job).
"I think he will be relying on that. He might have been told already to go and look for another club now because he might getting the sack. So it's not going good for him, bless him. I think some of the players have let him down.
"(Any in particular?) I just think the whole team in general. I think the whole team can hold their hands up, they’ve had a bad season."
A fan of Fernandes
Meanwhile, on the opposite side of the pitch, United will be leaning on captain Bruno Fernandes to produce a special performance and Gazza admits he's a fan of the Portuguese.
He said: "I like him. He’s got some engine and I like when he's playing, he’s also organising players and telling them where to go. It’s like having an extra manager, but he’s on the pitch!
"He scores some great goals and he really gets around the pitch. Both teams need to win this competition, I think just for a bit of a buzz."
Can't believe Tottenham's table position
On Spurs sitting in 17th place, Gazza admits the club's situation has left him stunned.
He continued: "I just can't believe it. Even Man United doing so bad too, just wow. Now I really try not to watch much football these days because I still miss it, but when I look at the league tables and things, I can't believe it.
"When I played, when a team wins the Premier League with five games to go, it's a bit disheartening. It’s happened to me twice. When the seasons coming to an end, I booked a holiday, I'm so excited. And two games to go and I've got injured.
"I spent my holiday in Princess Beach Hospital. Then you get some of your team mates who get shy of tackles. They won’t go in solid in case they get injured. You get a lot of that, I'm telling you!"
- Paul Gascoigne was speaking to Tribalfootball.com on behalf of ESportsInsider.com