The two sides meet in Paisley on Sunday, with Saints having failed to win any of their opening six league games and the Dons without a victory in their last seven matches in all competitions.
Glass took over from Derek McInnes towards the end of last term and is coming under pressure from sections of the Dons support, but Goodwin expects this weekend's opponents to enjoy an upturn in fortunes once their new faces have time to bed in.
He said: "Aberdeen are in a bit of a transition period. Derek McInnes was in there for quite a while and had relative success. He's a hard act to follow for Stephen Glass.
"Stephen has come in with a new philosophy, he's trying to blood some of the youngsters and he's signed a lot of the players. We had a similar situation here, because when you put a new group together it does take a bit longer than what you would like.
"When I look at the squad and the recruitment Aberdeen have done, I'm pretty sure once things fall into place they'll be absolutely fine.
"They've got a good keeper in Joe Lewis, they've added the likes David Bates and Declan Gallagher to the backline, Scott Brown is a fantastic signing, and Marley Watkins and Matty Longstaff will be big, big players for them.
"Once Stephen gets all those players fully fit and up to speed, I would expect them to start getting the type of results everyone expects them to get."