The 22-year-old was issued with a notice of complaint by the SFA after he was accused of diving to win a penalty in Sunday's match against Dundee at Dens Park.
From the resulting spot-kick Niall McGinn scored to seal a 1-1 draw for the Dons - a result that relegated Dundee from the top flight.
The SFA offered the two-match ban to Pawlett as a punishment and Aberdeen decided not to appeal despite disagreeing with the verdict.
A club statement read: "The action the club has taken does in no way mean we are not backing our player.
"While there was undoubtedly contact in the incident, we feel we would rather draw a line under the situation.
"The trial by television and subsequent coverage in sections of the media had almost sealed Peter's fate and as a result it was felt an appeal would have been fruitless."