The Blues sit third in the League One table and remain in the automatic promotion race with two matches remaining.
Kenny Jackett’s side sit four points behind leaders Luton and second-placed Barnsley but have a game in hand against Peterborough tonight (7.45pm).
Brown revealed finishing in the play-offs was Pompey’s chief aim at the start of the campaign.
With a top-two place still possible, though, the former Bristol Rovers man wants the Blues to finish the job and reach the Championship.
He said: ‘I’d have snapped your hand off (to be in this position) and most people would have.
‘But now we’re here it would be silly not to want to go all of the way.
‘The ambition at the start of the season was to get promoted.
‘The realistic aim was to finish in the play-offs given where the club is, with the budget and the other clubs in the division.
‘Realistically, that’s where most people see us. It’s been an improvement on last season.
‘Where we’d finish in the play-offs I didn’t know but I thought we’d be in and around that.’
If Pompey win their two remaining games against Peterborough and Accrington, they’ll finish on 93 points.
That still won’t be enough to go up automatically, though, should Luton or Barnsley fail to slip up.
But Brown stressed the Blues must concentrate on their own results and see where it takes them.
He added: ‘There’s a long way to go to finish on 93 points but there’s a long way to go.
‘We’ve got a tough game to go against Peterborough which is not a guarantee and Accrington at home is not a guarantee.
‘Nothing is a guarantee at this level and it’s the same for other teams.
‘We’ve got a lot of work to do and let’s see how lucky or unlucky we are.’