Rotherham should have had a penalty eight minutes before Murphy's goal as Karl Darlow clearly clipped Anthony Forde's ankles after some poor handling, but the goalkeeper got away with it and then produced a heroic save to deny Jerry Yates in the aftermath.
It might have been different had the Millers scored, but the remain nine points adrift of safety and with just one point on the road all season.
"I thought it was a penalty," boss Paul Warne said. "If Fordey had gone down he might have got it, but he was too honest and stayed on his feet.
"We limited them to very few chances in the first half, I thought the way we set up was working a treat. We went to toe-to-toe with them.
"My conversation at half-time was a lot more different to what I wanted to have and it was a psychological hit for the lads.
"They started the second half well and then the game was away from us. But I don't think our season will be decided on this game. They have got class and quality all over the pitch, they will be a Premier League club again next season.
"I am disappointed with how things went after the second goal, but I am not going to take anything away from them, I know what the result is."