Sheehan was taking charge of the Welsh side following Michael Duff's dismissal earlier in the week.
And they got off to a winning start thanks to goals from Charlie Patino and ex-Rotherham United player Jerry Yates, after Daniel Ayala was sent off after just 17 minutes.
Sam Nombe had pulled the Millers level on the stroke of half-time.
Sheehan said: "I am so proud of the players, staff and the whole football club. The support I've had from everybody has made that possible.
"We have stood up to a physical team. I think if we had been more clinical it could have been easier.
"They score from a long throw. They're a big physical team and we had to football our way out of it.
"We got the win. It has been a very difficult week and an emotional week. The overall feeling is pride.
Denne historien er fra December 10, 2023-utgaven av The Football League Paper.
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Denne historien er fra December 10, 2023-utgaven av The Football League Paper.
Start din 7-dagers gratis prøveperiode på Magzter GOLD for å få tilgang til tusenvis av utvalgte premiumhistorier og 9000+ magasiner og aviser.
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LUKE BOOSTED BY WALES ACE LIAM
Swans bid to mark new era in style...
MATT'S DELIGHT OVER RECORD
WYCOMBE boss Wanderers Matt Bloomfield hailed his history-makers after victory at Lincoln City.
TON-UP IAN ENJOYS HIS SPECIAL WIN
AN Evatt described his 100th win as Bolton boss as very special, although he needed Aaron Collins' injurytime goal to bring up the three figures.
DONS LACK A CLINICAL EDGE AS SADDLERS GRAB POINTS
NATHAN Lowe's strike inspired promotion-chasing Walsall to victory over AFC Wimbledon at the Cherry Red Records Stadium.
SUB GRIMES IS IN-SPIRED TO HEAD THE WINNER
CAPTAIN Jamie Grimes headed in a late winner for Chesterfield after a game of very few chances appeared destined to remain goalless.`
COBBLERS TEST IN TROPHY FOR POSH
HOLDERS Peterborough United have been drawn against fellow League One side Northampton Town in the Round of 32 of the newly-named Vertu Trophy.
HORNETS REMINDED OF GRAY'S BRILLIANCE
WAYNE Rooney expressed his delight as Plymouth extended their unbeaten league home run to six after Andre Gray's last-gasp leveller.
MARTI DOUBTING JOB AFTER DRAW
Rangers home run continues
BIG MAC'S ON TARGET TO SEE OFF THE TIGERS
LUTON boss Rob Edwards felt it was a very good day at the office as his team turned in a gritty performance to beat Hull.
Rohl confident Owls
DANNY Rohl said getting results is the only thing missing as his Owls were held at home by Cardiff.
