Chesterfield boss Paul Cook admitted his side got battered at Fratton Park.
The Spireites manager felt his team took a hammering from the Blues for much of the second half of Saturday’s clash.
And Cook admitted David Connolly should have had a penalty moments before he was sent off in the 2-0 win for the away side.
The Pompey striker was brought down by Liam Cooper – but the referee, Steve Bratt, bizarrely failed to point to the spot.
Connolly was then dismissed seconds later for a clash with Chesterfield midfielder Sam Hird.
Cook admitted that was pivotal in the game.
But he acknowledged his side were still hanging on until two late goals saw them steal the points.
He said: ‘The game swung on a couple of big decisions.
‘From where I was, it looked like a penalty for Portsmouth.
‘You have got to be fair and say what you see.
‘Then David Connolly got involved with something and got himself sent off.
‘I didn’t see the incident but nobody was arguing about it. In the second half, we didn’t play well.
‘We didn’t move the ball quickly enough and we were making bad decisions all over the pitch.
‘Portsmouth were the better side in the second half and they were battering us at times.
‘We were looking like we would settle for a 0-0 draw.
‘But we stuck in there and the one bit of quality we got into the box all afternoon, we scored.
‘And you have to say the big fella (Armand Gnanduillet) took his chance really well.
‘You’ve got to give the lads credit. It’s a fantastic result – not a fantastic performance – but a fantastic result.’
The win continues a fine start to the season for Chesterfield as they top the League Two table.
They have shown impressive form to pick up 13 points from their first five games.
But Cook feels it is too soon to be talking his side up as promotion contenders.
He said: ‘It’s far too early to talk about promotion just yet.
‘We’ve had a good start but there is a long, long way to go.