The Crystal Palace midfielder, who played under the manager at QPR, hit out when his ability under pressure was called into question after missing a penalty against Tottenham
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 networking website 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.