Palmer suffered the injury in the second quarter at Spotless Stadium, while Davis hurt his kidney after some accidental contact to his back from Swans midfielder Craig Bird.
That incident happened in the first term and Davis somehow played out the match, throwing himself into a number of contests and keeping Swans superstar Lance Franklin to just one first-quarter goal.
The club is still unsure of the exact nature of Davis' injury or how long the co-captain will remain in hospital, but teammate Heath Shaw paid tribute to his courage on Tuesday.
"(Franklin's) obviously a big part of the Swannies going forward and we knew we had to nullify him," Shaw said.
"Phil Davis, along with the backline, managed to do that and it's total credit to Phil.
"With the injury he's got, to play out the game the way that he did was just amazing.
"The state he's in now we're not too sure, he's still in hospital and we're not sure of the extent of it just yet, but he played out the game and went straight to hospital after keeping 'Buddy' to one goal.
"It was an amazing effort and went a long way towards us winning that game."
Palmer showed some good signs before his injury and it is more bad luck for the 25-year-old, after a calf injury and a recurring foot problem restricted him to just 11 games last year.
Yet there was still plenty of good news to come out of the game for GWS, including the display of key forward Jonathon Patton.
The club's No.1 pick in 2011, two serious knee injuries kept Patton to just 10 appearances over his first two years in the AFL.
Patton finished with 13 touches and three goals while spending 84 per cent of the match on the ground in an extremely encouraging performance.
But the 20-year-old, who targeted round one ever since he suffered the injury in round three last season, says he is still only around 75 per cent fit.
"I'm probably still a fair way off (full fitness)," he said.
"I'm still getting the odd cramp here and there and only did the last three or four weeks of pre-season really.
"I've still got a lot of things to work on in terms of my fitness and all that, but it'll come with the more games I play and the more confidence I get with my body."
Patton certainly didn't seem to be suffering any cramp when he kicked one of the match-sealing goals late in the final term on Saturday.
"I got a bit excited and did a bit of a Setanta O'hAilpin with the celebration," Patton joked, referencing his excitable former teammate.
"It was a bit embarrassing looking back on that, but it just showed how much we all cared at the end of the game and how much it all meant for us."
