Leam Richardson believed Pompey’s superiority eventually counted as Carlisle were defeated 1-0.
Michael Smith grabbed the only goal of the game when he finished from a tight angle in the 57th minute, after Kyle Bennett’s shot had been saved.
Adam McGurk also struck the post in a vastly-improved second-half display from Paul Cook’s men.
Following a flat opening 45 minutes, the Blues went through the gears to win the fixture after the break.
And assistant manager Richardson felt the quality finally came through for Pompey.
He said: ‘Carlisle came and set up a certain way and it was up to us to set our own tempo and lift our own crowd in what we did.
‘That was echoed at half-time and the lads came out with intent.
‘When you have two contrasting teams and there is a lot to play for, normally if you stick to what you believe and work hard then the team with the better quality will come out on top.
‘We feel in our dressing we have that and thankfully today have come out on top.
‘We had numerous shots and crosses in the second-half and put them under pressure.
‘Then when questions were asked at the other end they didn’t capitalise and we kept the back door shut for another clean sheet.’