Danny Cowley’s men returned to winning ways on Tuesday night, running out 3-0 winners on the night against the Reds.
Skipper Clark Robertson was on the scoresheet for the first time for the Blues, netting against his former side with 35 minutes on the clock.
Former Millers loanee George Hirst ran riot in the second period – assisting Marcus Harness before notching his 11th of the campaign to cap off a man-of-the-match performance.
The triumph leaves Pompey 10th in League One with five games to go, while Warne’s promotion-hunting side remain third after a third straight league defeat.
And the Millers boss believed his side were ‘outplayed and outfought’ – before apologising to the 301 travelling faithful.
Speaking to Rotherham’s official website, Warne said: ‘The changes we made didn’t have the impact we wanted – and for us to concede off two set-pieces is unheard of.
‘There wasn’t much in the game until they scored, in fairness they looked a little bit brighter, but there wasn’t a lot in it.
‘It was a bad night and we have to take our punishment at the end. There’s no hiding from it, I apologise wholeheartedly to the away fans who travelled.
‘We’ve had a little bit of a slide and need to put a flag in the ground now.
‘I haven’t got an excuse book. I think we’ve been outplayed and outfought, which isn’t like us.’
The Millers' impressive Jordi Osei-Tutu came off in the 84th minute following a collision with Gavin Bazunu as the keeper came racing out of his area.
The 23-year-old, who required on-pitch treatment before his withdrawal, left Fratton Park wearing a boot.
Yet no foul was given against Bazunu for his part in the unfortunate proceedings.
Warne added: ‘Jordi is on crutches and a boot as we speak, I thought he’d broken his foot at first.
‘We’ll have to see how he is, but it doesn’t look good.’