Alisson was injured while making a clearance and was forced to limp off in the second half of the Premier League clash at Selhurst Park.
Czech international Vitezslav Jaros, 23, came on to replace Alisson, with Liverpool boss Arne Slot admitting he does not expect to have his first choice available for a while.
Alisson has been hampered by hamstring injuries and will miss the Premier League leaders' game against Chelsea following the forthcoming international break.
"What I do know is that when a player walks off like he did, it normally means he's not in the Brazil squad and I don't expect him to be in the team for the first match we play after the break," Slot said after Diogo Jota's ninth minute goal sealed Liverpool's sixth win in seven league games this season.
"We have to wait and see but it will be a few weeks for him to be back. I think it is, yes (his hamstring).
"He's clearly our number one, he's the best goalkeeper in the world. It's always a blow when he gets injured, not only for him but us as a team."
Slot endured another injury blow when Alexis Mac Allister was replaced by Dominik Szoboszlai at half-time due to a groin injury.
Unclear how long Mac Allister will be sidelined for, Slot said: "How bad that is, it's not for me to judge at this moment.
"He felt it and said 'it's not good to keep on playing because it could be made worse'.
"It's difficult for me to say if he can play for Argentina. It was in the groin area."
