Jamie Lindsay fired home four minutes from time as the Millers' moved above Derby, who slip to second bottom of the table.
It was far from an ideal start to his reign for the former Manchester United and England captain, who gave an honest assessment of side's under-whelming performance.
"Today Rotherham outfought us," said Rooney.
"Our quality on the ball and our concentration levels weren't where they should be.
"That's the disappointing thing and, if I'm being honest, I don't think we deserved anything from this game."
At the other end of the table, Norwich remain well on course for an immediate return to the Premier League thanks to a fast start in a 2-1 win at Cardiff.
Grant Hanley put the leaders in front after just four minutes, nodding in at the far post after a flick on from a corner.
And it was 2-0 after 20 minutes as Todd Cantwell rounded off a slick counter-attack by slotting into an empty net following a smart save from Alex Smithies.
Joe Ralls gave Cardiff hope by thumping into the bottom corner from 12 yards after 65 minutes but the hosts were reduced to 10 men five minutes later when Marlon Pack was shown a second yellow card and slipped to a fourth successive defeat.
Second-placed Swansea can close the gap at the top back to four points with victory later at Barnsley.
Bournemouth missed the chance to go second after a 1-0 loss at home to Luton.
The Cherries' task was made more difficult when Jefferson Lerma was shown a straight red card after 26 minutes for catching Tom Lockyer in the face with a stray arm while competing for a header.
Bournemouth pushed to overcome their numerical disadvantage but Luton capitalised as the hosts tired when Kiernan Dewsbury-Hall curled the winner into the bottom corner 23 minutes from time.
Watford returned to the playoff places with a 2-0 win over Huddersfield.
Tom Cleverley gave Watford a 54th-minute lead by capitalising on indecisive defending from Huddersfield.
Alex Vallejo attempted to pass the ball back to Ryan Schofield, who hesitated as Cleverley closed in and beat the goalkeeper to the ball to slide in from six yards.
Joao Pedro made sure of the points 10 minutes later, tapping in at the far post from Kiko Femenia's cross.
Sammy Ameobi struck twice as Nottingham Forest secured back-to-back wins for only the second time this season with a 3-1 victory against Millwall.
Birmingham manager Aitor Karanka enjoyed a successful return to the Riverside as Scott Hogan struck to earn the Blues a 1-0 win and prevent Middlesbrough from moving into the play-off places.
A 1-1 draw did little to aid Stoke and Blackburn's playoff hopes.