Alisson was replaced in the 79th minute of the contest after suffering up a hamstring issue, while Liverpool picked up a further fitness blow at Selhurst Park, with Alexis Mac Allister sustaining a groin problem in the first half.
Slot has all but ruled Alisson out of Brazil's upcoming matches and said that the goalkeeper is unlikely to be available for the clash with Chelsea on October 20, but the issue suffered by Mac Allister is not as serious.
"The latest is that we don't know but what we do know is that if a player walks off like he did, that normally means that he is not in the Brazil squad and I don't expect him to be in the team in the first game we play after [the international break]," the Liverpool boss told reporters at his post-match press conference.
"We have to wait and see, but it is going to take a few weeks I assume for him to be back. I think it is [his hamstring]."
Alisson, Mac Allister both picked up injuries against Palace
Addressing Mac Allister, Slot added: "He went off because of an injury, but how bad it is is difficult for me to judge in this moment.
"He could have continued playing, like you saw, because it didn't happen one second before half-time, but he felt it a bit too much and he said he didn't think it was good to keep on playing because you never know if you will make it worse.
"Now, what is the exact situation, can he go to Argentina? Can he play over there? That is difficult for me to tell you now. [It's an issue] in his groin area."
Liverpool secured all three points against Palace courtesy of a ninth-minute Diogo Jota effort, and they are currently top of the Premier League table, one point ahead of second-placed Manchester City.
Slot sets Liverpool record with win over Palace
Slot also revealed his delight at having the best winning start of any Liverpool boss in history, posting nine victories from his opening 10 games at the helm.
"It definitely is [very satisfying]. And it's actually also quite special if you know how many great managers Liverpool had. But I also said last week I think that I hope they don't only remember me in one, two, three, four, five years only for this," he said.
"We are hoping to do more special things than this. And it also says the luck I had that I inherited a very good squad and very good staff to continue getting the results that Jurgen [Klopp] had here as well."
Liverpool have been victorious in each of their last six matches in all competitions, while their only loss of the season proved to be a 1-0 home reverse to Nottingham Forest on September 14.