The Western Australian club fought back from a goal down to equalise before being dumped out of the finals race in a penalty shootout that was dominated by Phoenix goalkeeper Liam Reddy who made two saves.
Despite the loss, however, Glory skipper Jacob Burns was proud of the way his teammates went about it but did admit it was a sour way to go out.
"You'd probably want to lose in normal time really," he said.
"But I'm extremely proud of the boys. I thought we did ever so well. I thought we did enough but you've got to take your hat off to Wellington.
"They've had a very good season and a fantastic crowd out here today. It just wasn't our day. It's a horrible way to go out.
"We've had everyone writing us off and we showed that in 120 minutes that we're a good side," he added.
"We played them off the pitch but if you don't put the ball in the back of the net it normally comes back to bite you and today it did."