The 22-year old was charged by the Scottish Football Association for simulating in order to win a penalty in the 1-1 draw with Dundee on Sunday.
The SFA offered Pawlett, who has previously been suspended for diving, a two-match ban which he has since accepted.
"The action the club has taken does in no way mean we are not backing our player,” read a Dons statement.
"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."