Puncheon, who played for Warnock during a loan spell at QPR in 2011, made a number of allegations against the 65-year-old on the social media platform in January.
Warnock had questioned Puncheon's ability to handle pressure while speaking as a pundit on talkSPORT after the winger had missed a penalty in Palace's 2-0 defeat at Tottenham.
Puncheon responded with a string of tweets, which were subsequently deleted, questioning Warnock's integrity.
The 27-year-old was charged with failing to "act in the best interests of the game and/or acting in a manner which was improper and/or using abusive and/or insulting words", which contravened FA Rule E3(1).
And the FA confirmed on Tuesday that Puncheon has now been fined after admitting the charge, with the former Southampton man also being warned as to his future conduct.
Get the best features, fun and footballing frolics straight to your inbox every week.
Thank you for signing up to Four Four Two. You will receive a verification email shortly.
There was a problem. Please refresh the page and try again.