The Sky Blues sit third on 38 points (goal difference +8), ahead of Melbourne City (+1) on goal difference, but are three points back from Auckland FC (41, +14), who play on Sunday, while leaders Newcastle (45, +12) are out of reach.
Patrick Kisnorbo's Sydney would need Auckland to lose against Central Coast, then beat Steve Corica's charges in their final game to finish top two.
Fighting for a home elimination final appears more likely after a costly performance at Allianz Stadium on Saturday night.
"It was a well-fought game but we were just flat in certain moments of the game and it's just disappointing not to get the three points," Sydney's Socceroos midfielder Paul Okon-Engstler told Paramount Plus.
"... I think it's another opportunity missed."
With Socceroos boss Tony Popovic among those in the stands, the home side dominated play but failed to ignite.
Al Hassan Toure sparked the contest in the 20th minute when he burst down the right then forced a sharp save from Matt Sutton.
A scuffle broke out in the 36th minute after Sydney skipper Rhyan Grant went in with a studs-up, two-footed challenge on Sam Sutton - and can consider himself lucky to only see yellow.
"To be fair I'm not sure about the rule - two feet off the ground, maybe it's a red," Perth coach Adam Griffiths said.
"But it was a dangerous tackle - I think Rhyan knows that - but I said it was a good tackle to him."
Okon-Engstler ripped a long-range shot over the bar in first-half added time, while Jaiden Kucharski skidded a fierce effort just wide of the post shortly after.
Sydney attempted to up the ante after halftime and Sutton pulled off a sublime save with his leg to deny Apostolos Stamatelopoulos in the 55th minute.
Toure went on another terrific run just after the hour mark but dragged his shot wide and the Socceroo was visibly frustrated and unhappy when substituted in the 68th minute.
"You can be frustrated but it's the way you sort of show your frustration," said Kisnorbo.
"He'll be disappointed if he sees that again - and I won't have that in the team, because everyone gets frustrated, including myself."
Glory's Sebastian Despotovski blasted a golden chance over the bar in the 78th minute, while Sydney young gun Akol Akon headed a Ben Garuccio cross wide two minutes later.
Neither team had the clinical edge required to find a late winner.
The 10th-placed Glory finish their campaign at home to 11th-placed Brisbane next Saturday.
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