Odabert scored twice, with Maddison also netting, as Spurs won 3-1 to reach the quarterfinals 3-2 on aggregate.
Postecoglou said of Maddison afterwards: "Yeah, I thought all night he was really good. I think all those four leaders felt like it's their time now. It's been really tough for them, it's been really tough for all of us, the whole club but particularly the players. I thought that Madders, when we needed the quality, he was there tonight and made all the good decisions for us. Worked hard for the team, which was so important.
"I think from my perspective it now allows us to have this solid core of players, our best players, that are available, getting to fitness, but we also have this ability to put people on who can also impact games which was important today."
The manager also said of young winger Odobert: "Super pleased for him because he's worked awfully hard. I'd be surprised if I have to explain why I selected him, if you didn't see that today... I was excited when we signed him. He's one of these players who has the ability to take players on, find space, great technician and super pleased for him to get his goals. He's worked hard silently and to get back in the team.
"Obviously he came to a new club, a big club and big move for him and it didn't work out for him through no fault of his own, through the injury and it's been frustrating for me not to be able to showcase him and know how much he can develop and that's just the starting point for him. He's still working his way to full fitness. When you look at the likes of him and Lucas and Archie and two or three others we've got, there's some enormously exciting talent there."