Scotland international Christie was charged with violent conduct following Celtic's 2-1 loss in the fixture, and a hearing on Monday upheld a two-game ban, with a further game added as a result of a previous red card against Livingston.
Christie had been shown a yellow card by referee Kevin Clancy earlier in the match, but initially escaped punishment over the incident with striker Morelos, who was sent off for a second bookable offence in added time of the second half.
Celtic Football Club statement regarding Ryan Christie's sanction ⬇️— Celtic Football Club (@CelticFC) January 6, 2020
Scottish Premiership leaders Celtic said in a statement released on Monday: "Given the recent treatment of Celtic players and the lack of sanctions being imposed on those responsible, the fact that a sanction has been imposed on Ryan for the incident in question demonstrates a worrying lack of consistency in the Scottish FA fast track process.
"Naturally, we will be contacting the Scottish FA regarding our concerns. Scottish football deserves a disciplinary process which is fair, consistent and fit for purpose."
A year ago, Celtic said Christie was the victim of a similar offence -- committed by Morelos -- but the Colombia international received no sanction.
As a result of the ban, midfielder Christie will miss league games against Kilmarnock and Ross County this month, as well as a Scottish Cup tie with Partick Thistle.
The 24-year-old was already a doubt for those fixtures, however, after undergoing groin surgery due to an injury sustained in the Old Firm derby.