The 31-year-old midfielder is the latest name out for the Swans, whose injury list has climbed to 14.
Adams will spend three to four weeks on the sidelines after sustaining a hamstring injury in the fourth quarter against Hawthorn on Friday.
The midfielder was dropped ahead of the Swans' finals series last year and was set to prove himself after Errol Gulden was ruled out of Opening Round.
The Swans host Brisbane in a grand final rematch on Saturday and Cox must rethink how he's going to set up his team, already missing a handful of big-name players.
"Unfortunately for Taylor he's hurt his hamstring. He had scans on Monday and he'll be out for three to four weeks," Cox said on Tuesday.
"He's an experienced player so he'll deal with it, but we thought he was going to play an important role for us at the start of the year.
"We had a couple of concussions and a shoulder injury, we got knocked around in the VFL as well."
Tom McCartin was also missing from Swans training on Tuesday.
The newly rotated forward failed to make an impact against the Hawks, recording just seven disposals and one goal.
Despite the defender being moved up front in the pre-season, Cox said goal-scoring was not down to just him, rather the whole team.
"When Tommy (McCartin) is in front of the ball, to hit the scoreboard that's one thing, but for him it's also about presenting outside, and letting Joel (Amartey) play different," he said.
"We've got to make sure we're around the contest. (Brisbane) is the number one contested side.
"Our work in the centre, forward is an area we need to work on, but also our intensity around the ball. It dropped around the second quarter (on Friday)."
In positive news, Tom Papley will be raring to go on Saturday, despite the forward seen hobbling on his fragile ankle against the Hawks.
Papley missed much of the Swans' pre-season after spraining his ankle, and was tested before being cleared to play last Friday.
"Papley is fine. He will train fully this week and be good to go," Cox said.
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