The Europa League success was Tottenham’s first trophy since a 2008 League Cup win, with a Uefa Cup triumph back in 1984.
Postecoglou has come under pressure this season with Spurs currently fourth from bottom in the Premier League.
But former Northern Ireland international Armstrong added: “I think it could be a turning point for them for next season and I think they will make around £100m.
“With that in mind, I think they can now get themselves into the top six or seven in the table for next season and the fans will be looking forward to that and obviously playing Champions League football.”
While he admitted it was not a match that will be remembered for its outstanding football, he felt Spurs produced a solid team effort at the San Mames stadium.
“The back four looked really solid. I was a little bit worried about the goalkeeper, but he made three or four great saves,” he added. “On the night, it was a good team performance, everybody worked hard.
“I didn’t expect them to defend that deep for that long. I thought they would maybe have staged a few more counter-attacks and pushed forward a bit more.
“What a crazy season it’s been for both sides though. It’s the lowest I can remember them [Spurs] finishing, apart from the year they were relegated back in 1976-77. [Manchester] United have obviously struggled hugely in the league too.
“But this win will certainly give them (Spurs) confidence and belief. I’m pleased for so many of the players too, who will maybe never get an opportunity like that again, to play in Europe and to win a final.”