The 31-year-old forward struck a post from the spot on 59 minutes but headed home seven minutes later as the Blues ran out 1-0 victors against the Trotters at Fratton Park.
Pitman admitted players always run the risk of missing when stepping up to take penalties - yet was relieved to redeem his error by going on to grab the winner.
He was delighted to eventually give the Fratton faithful something to cheer after an uncharacteristic miss from the spot.
Now Pitman wants Pompey to build some confidence and momentum on the back of just a second league win of the season.
He told the club website: 'If you take penalties you’re going to miss some of them.
'It was disappointing to hit the post, but then pleasing to score the winner. 'My record for Pompey is pretty good – I think it’s only the second I’ve missed – but you do feel like you owe the fans something. 'Fortunately, Bolts has then sent in a great cross and I’ve managed to put away the header at the back post. 'If we want to achieve our aims then we need to go on a run sooner rather than later, so we need to build some momentum and confidence.
‘We’ve struggled a little bit for results in recent weeks, so it’s obviously a really big win for us.
'Everything we played forward just seemed to run out of play, but we were a lot better after the break.’
Bolton remain rooted to the bottom of League One on minus nine points following the defeat.
They were deducted 12 points in the summer after entering administration, but were on the back of successive draws before defeat at Pompey.
But Pitman believes they possess Championship-quality players in their squad and praised their efforts at Fratton Park.
‘You have to give credit to Bolton for the way they performed the first half and I think the wind made it really difficult as well,’ he added.
'I know they’ve had some heavier defeats earlier in the season, but you look through the spine of the team now and there are Championship players.
'They’re certainly no mugs and I don’t think the team they put out at Fratton Park will get many tonkings.'