Puncheon - whom Warnock signed on loan when manager at QPR in September 2011 - spurned the chance to give relegation battlers Palace an early lead at White Hart Lane when he blasted his spot-kick horribly wide.
Spurs went on to win the match 2-0 as the Eagles were left bottom of the Premier League.
The 27-year-old came in for criticism from many commentators over the weekend, but took exception to comments from Warnock in his role as a pundit on talkSPORT.
Puncheon, who is on loan at Palace from Southampton, has since deleted his posts - copies of which have been seen by Press Association Sport.
Warnock, sacked by Rangers in November 2012, revealed he had been alerted to the matter and was now considering his next course of action.
The Football Association, meanwhile, is also set to seek further information. A spokesman confirmed: "We are looking into it."
Warnock maintained the matter was being "addressed directly" with Puncheon.
He said in a statement: "The first tweet 'everyone is entitled to their opinion' I haven't got a problem with, but moving on from this is his later tweets. He's made comments I know nothing about. If it has been suggested I have done anything untoward I confirm I most certainly have not.
"I notice Jason has removed his tweets. The matter is being addressed directly with him on my behalf. In the circumstances there is nothing more for me to say."
Puncheon left only the following post on his official Twitter account.
"In the wake of a bad penalty and people's opinions and banter which I accept @mattletiss7 on @talkSPORTLive this morning gets it right."
One earlier Tweet had read: "Everything else is banter and opinions and as a man I will live with that which is fine but I will not live with his opinion."
Warnock had not held back in his criticism of Puncheon during his comments on live radio.
"There's no way I would've trusted him with a penalty. You've got to have somebody a little bit more cool, and he's not like that, Jason," he said.
"He can whack a 35-yard free-kick in here and there but a penalty, with all the pressure on him at a place like White Hart Lane - not in a million years for me."
Warnock added: "I think a centre-half might have done a bit better! Obviously, he never meant to put it up there."