Sakho had to be substituted after suffering the injury in a challenge on striker Harry Kane and the on-loan centre-back requires a scan to determine the extent of the problem.
"We're unable to say what the extent of the injury is at the moment, but it didn't look too clever with the way the knee hyper-extended," Allardyce told reporters on Thursday.
"But let's wait for the scan and then probably contact Liverpool and see what the situation is, depending on how serious the damage is. Until we have had the scan, we can't really speculate on the if, when and how on what the seriousness of the injury is.
"I don't want to speculate regarding what it is or isn't, but it didn't look too good the way the knee twisted. We hope it's not the cruciate. It could be medial or lateral, but it was certainly a hyperextension of the knee. We will see after a scan.
"The scan will give us an indication of the seriousness of the injury and then we will speak to Liverpool. I would like to think it is not that serious, and that he will get back before the end of the season, but I am not sure."
Christian Eriksen's long-range strike consigned Palace to a 1-0 defeat on Wednesday and Allardyce believes his side need three more points to guarantee Premier League survival, as they prepare for Saturday's home game against Burnley.
"We were fantastic in the first half and matched Tottenham all the way through that time - an Eriksen wondergoal settled it," Allardyce added. "Had we been fresher maybe we would have closed Eriksen down better. It's done now, we've got to realise the importance of Burnley.
"We want to beat Burnley to get over that 40-point mark and put it to bed once and for all. It will require a big, big effort. Patience is paying off for Burnley. Sean [Dyche] has provided a recruitment and training policy that delivers. He's done a fantastic job.
"Three points is going to do it. Mathematically not quite, but I don't think you'll be caught on 41 points. We'd want to do it ourselves if we can, rather than rely on other clubs.
"Every club in our position has pencilled in plans for 17/18. You can rub them out and write them in ink when you're safe. You can survive in the Premier League if you build a great infrastructure. Growing slowly but surely can work due to the money you get."