Joe Mattock headed home substitute Michael Smith’s cross in injury-time to hand the Millers victory and inflict a third defeat on the road for the visitors.
Pompey thought they had weathered the storm before the former Fratton Park duo struck late on, after the home side turned the screw on them in the second half.
The Blues definitely shaded the first half after chances for Jamal Lowe, Kal Naismith and Brett Pitman.
However, they were up against it in the second half.
And just when they thought they had dome enough to claim a deserved point against a promotion-chasing rival, up pounced Mattock to nod home the winner.
Jackett said: ‘It is sickening (to concede like that).
‘An injury-time winner, which has turned it for them in a second half where they’ve put us under pressure early on and we rode the storm well and defended very well.
‘First period we had the better chances and didn’t take them and it brought the pressure on.
‘A 91st-minute goal to win the game, where it’s been our goal-kick, we’ve kicked it out - a series of events then right through to a far post header from four yards out that has got the points.
‘You can’t say it’s a lack of luck, you make your own luck, and they’re frustrating and disappointing late goals like that.
‘At times we haven’t got enough experience to kill them off.’