Brian Howard will be relieved of penalty duties after his spot-kick miss at MK Dons.
Howard missed a crucial penalty in the first-half as Pompey drew 2-2 against the Dons.
That made it two failed efforts from 12 yards on the bounce after he also squandered a similar opportunity against Scunthorpe last weekend.
Appleton explained someone else will take the next penalty the Blues are given.
Strikers Wes Thomas and Izale McLeod are favourites to be handed the role at present.
Appleton said: ‘I think that’s sensible really (to find a new penalty taker).
‘Brian was unlucky the ball’s hit the post but I would imagine one of the front players will be champing at the bit to get the next one.
‘I’d be very surprised if one of the strikers doesn’t want to claim it.
‘I’ll be passing on responsibility to one of them.’
Saturday’s clash with MK Dons also proved to be a tough afternoon for Adam Webster.
The 17-year-old made his third start in a week as he continues to make the breakthrough into the first-team ranks.
Webster scored an own goal and lost Darren Potter for MK Dons’ leveller, after a sound general performance.
Appleton believes he would have learned a lot from the game.
He said: ‘That’s the highs and lows of football.
‘He was delighted on Tuesday.
‘He switched off from the set-play and Brian got a little touch at the near post which diverted it into the path of Adam.
‘The guy who scored the goal for them was Adam’s man.
‘That’s the type of day he had. He made two mistakes which have cost us two goals.
‘But I thought his general play was magnificent for a 17-year-old.
‘Hopefully it’s a good education for him, he learns from it and it doesn’t happen next time.
‘If he keeps making sure that doesn’t happen then that’s good.
‘You only have to look at his general play.
‘For a 17-year-old coming into the team in difficult circumstances, he’s done really well.
‘Everyone can see what a bright future he has.
‘He came back from the own goal and had an attacking run right after.
‘That shows his true character. He’s a good lad and a lovely player.’
– JORDAN CROSS