Pompey have yet to decide whether to appeal David Norris’ red card.
The midfielder was sent in the 65th minute of Saturday’s 1-0 defeat following a foul on Winston Reid.
It was one of several controversial decisions made by referee Kevin Friend.
The Leicestershire official was confronted by skipper Liam Lawrence at the final whistle before being booed off by sections of the home fans.
Appleton himself thought Norris’ dismissal was ‘harsh’.
Lodging an appeal with the Football Association remains a realistic option for Pompey.
But the Blues boss is concerned failure in that bid could see the mandatory three-match ban increased.
He said: ‘I have seen the replays, I think we have been harshly done on both that and the penalty.
‘Whether we will appeal or not, I will have to speak to the powers that be and see.
‘What I don’t want to do is put David in a position where we lose him for four games instead of three games.
‘If you act too quickly after the game your emotions are running too high. Sometimes you cannot see through the mud, so to speak.
‘The thing that didn’t help David at the time was he left the ground – but I don’t think it was a two-footed challenge as such.
‘He has come in from the side and genuinely tried to stop the lad passing the ball forwards.
‘It’s the type of tackle you sometimes see centre forwards do when they are stopping defenders trying to play the ball down the line.
‘Although, the biggest disappointment is I have never seen a red card pulled out of a pocket so quick in my life.’