The Zaire-born midfielder found himself dropped for the first time in the Barclays Premier League this season but responded by netting the opening goal just seven minutes after replacing Chung-yong Lee.
Coyle said: "Fabrice scored a great goal. It was a big decision for me to leave him out because he has started every game for me. It shows I'm not afraid to make the big decisions."
He added: "It would have been easy for Fabrice to sulk but he didn't. He came on and scored a wonderful goal."
Despite Mark Davies' sending-off and an 87th-minute equaliser from Mame Biram Diouf, Coyle's men refused to accept a point and were rewarded when Stuart Holden volleyed a stunning winner one minute later.
Muamba's 65th-minute opener had got the home side back on track after their bright start had faded away to allow Sam Allardyce's Rovers to take control of the game towards the end of a dull first period.
Coyle said: "What I loved was that having lost an equaliser so late in the game and being down to 10 men, it would have been easy to feel sorry for ourselves.
"But with this group their first instinct was to go forward to try to win it, even with 10 men. What it showed me was that we have a tremendous spirit and desire to go and work for each other and to stand up and be counted."
Allardyce was moaning loudest about Davies' 56th-minute dismissal for an apparent elbow on Phil Jones, as the game turned at that moment with the 10 men in the ascendancy.
"I thought we were better when we had 11 versus 11," said Allardyce. "I didn't see a threat until they went down to 10 men. The disappointing thing is throwing the point away at the end."
Source: PA
Source: PA