Last year's grand finalists kept their slim top-eight hopes alive with a hard-fought 11-point win over Fremantle at the SCG on Sunday.
It marked Sydney's third win from their past four games, improving their record to 7-9 under first-year coach Dean Cox.
But such is the gulf between the top nine and bottom nine teams this year, Sydney still find themselves three wins adrift of eighth spot.
Even Fremantle, boasting a 10-6 record, aren't currently in the top eight, highlighting just how hard it will be for Sydney to reach the finals this year.
Swans star Errol Gulden concedes his team need to win all of their remaining seven games to make the finals.
Sydney will start as favourites in Sunday's clash with St Kilda at Marvel Stadium, and will be expected to win games against North Melbourne (home), Essendon (home) and West Coast (away).
But matches against GWS (Engie Stadium), Brisbane (Gabba) and Geelong (SCG) loom as trickier tasks.
"We still think we're capable of playing finals," Gulden told reporters on Wednesday.
"I think we'll probably have to win every game.
We've got to take care of the Saints this week, and fingers crossed the teams above us lose a few games as well."
Defender Dane Rampe (calf) is a chance to return against St Kilda, but Joel Amartey (adductor) and Tom Papley (hamstring, 2-3 weeks) have been ruled out.
"I was pretty shattered for Joel after the game. It's a pretty long injury, so it's most likely his season over," Gulden said.
"It's disappointing for Paps as well. I'm sure he'll do everything he can to get back as soon as he can.
"You've seen the difference he makes to our team and the way our forward line functions when he's out there.
"I spent a lot of time with those boys in rehab, and to see the amount of work that they put in for them to be injured one or two games back into their return, it's super disappointing for them, and I feel for them."
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