The Reds were on the back foot from the 4th minute when Doyle opened the scoring and went two goals behind to an Andy Gray penalty early in the second-half.
McGugan gave Forest hope and the home side had to withstand some concerted pressure before sealing the game through Butterfield late one.
"I thought there was only one team going to win it and we got caught by a sucker punch when we were pushing forward for an equaliser," said assistant manager David Kelly after the game while home boss Mark Robins commented: "After the goal Forest had us under a lot of pressure because they're a good side, they've got players with pace and power.
"In the second half they put us under a lot of pressure with long balls and apart from their goal I thought we did particularly well. When they came back I made a few changes and Jacob Butterfield scored a good goal.
"I thought it was a good win because we have two difficult away games. We did very well and I am delighted."