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.
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