The 125 million-pound striker broke the deadlock with his second league goal for Liverpool, having come on at halftime, but his foot got caught between Micky van de Ven's legs as the Spurs defender dived to block his shot.
Isak spent several minutes on the floor before walking off gingerly with the help of two members of Liverpool's medical staff and Slot said his "gut feeling" was Isak's injury could be a serious one, though he tried to be optimistic.
"I don't have any news on him, but if a player scores and then gets injured and doesn't come back on the pitch and also doesn't try to come back ... that's usually not a good thing," he told reporters.
"I cannot say anything more than that, that is just gut feeling, but nothing medical to say about it."
Conor Bradley's return to the side also lasted just 45 minutes after he hobbled off following a collision with Djed Spence and did not return for the second half, replaced briefly by Isak.
Liverpool still struggle
Liverpool seemed to have wrapped up the win when Hugo Ekitike doubled their lead, but substitute Richarlison set up a tense finish with an 83rd-minute goal for Spurs, down to 10 men after Xavi Simons' first-half red card.
Captain Cristian Romero then picked up a senseless second yellow for kicking out at Ibrahima Konate in the 93rd minute to leave Spurs with nine, though Liverpool were still indebted to goalkeeper Alisson for preserving their three points.
Slot said he thought Liverpool were improving after a summer of upheaval, which contributed to a dreadful run of form, though the Reds are now unbeaten in six in all competitions.
"We made so many changes in the summer that it would take time," Slot said. "Maybe because we won the first five or six games, everybody thought this would just go so easily."
He added: "I think it's never been as bad as people said. But it's also true that we are definitely not perfect yet."
Liverpool's fragility after conceding and how they laboured against the nine men of Spurs will, however, concern the Dutchman, who admitted "it looked as if we were down to nine and they (had) 11 because it was attack after attack after attack".
"It wasn't perfect today, especially not in the last 10 minutes," Slot said. "But in the meantime, we pick up points and I see the team developing in the way I would like to see."