Brighton continue to tread a cautious path with their young wing back who is returning to full fitness after a lengthy hamstring injury.
Experienced campaigner Pascal Gross played on the right side of the midfield but his solid performance was overshadowed by his first half penalty miss.
Lamptey, who continues to be linked with a move to Man United this transfer window, is said to be fit and should be available for Tuesday's clash against Chelsea.
"Tariq was not ready to start," said Potter after the match. "He missed a bit of training. He had a tight abductor so he was not ready for 90 minutes.
"Pascal did really well at West Brom and we were without Enock [Mwepu] and Yves [Bissouma]. We wanted to play that extra midfielder player in there.
"He contributed really well to the first half performance but then missed the penalty but that's life sometimes. He was the designated penalty taker today, he has scored penalties before but not today.
"He [Lamptey] is fine he just missed a bit training. Obviously with Tariq and what he has been through we went on the side of caution. He had a couple of days training and with some time today it would have done him some good.
"He will be available, providing there is no problem, for Chelsea. I have not been to the medical room as yet but if there is no further problem he will be okay for Chelsea."
Brighton, who dominated most of the match, clawed their way back from a goal down after Conor Gallagher had given the visitors a second half lead.
Lamptey helped Brighton push to the end but it was Neal Maupay's cut back that was turned in to his net by Palace defender Joachim Andersen that sealed the point.
Brighton were twice denied an opener during a crazy spell in which they missed a penalty and had a goal disallowed.
Gross’ tame attempt from the spot was repelled by Palace goalkeeper Jack Butland after Joel Veltman was adjudged to have been fouled by Will Hughes at a corner following VAR intervention.
Palace’s travelling fans, who threw a flare onto the pitch before Gross’ kick, had barely finished celebrating the save when Maupay put the ball into the net moments later.
Referee Robert Jones was once again called to the pitchside monitor and subsequently ruled Maupay had bundled the ball out of Butland’s hands.
Potter also appealed for a penalty at the end when Lamptey appeared to be bundled over in the box but said it was more hope than expectation.
"I was just trying," Potter said. "You never know. I was having a bit of a luagh with their guys. You never know when Tariq goes down. But I think it more in hope than any real conviction."