Coyle was dismissed on Tuesday after nearly three years in charge at the Reebok Stadium with the Trotters sitting 18th in the Championship, just above the drop zone, following last season's relegation from the top flight.
Bolton have struggled since and Saturday's last-minute loss at Millwall left them with a mere 11 points from 10 matches.
Muamba was forced to retire from football in August after collapsing on the pitch following a cardiac arrest while playing for Bolton in March, with Coyle widely praised for his subsequent support for the player.
Doctors revealed that the 24-year-old's heart had stopped beating for 78 minutes, but he was eventually stabilised and went on to make a recovery which some described as "miraculous".
"Owen was very supportive to me and I am grateful for that," Muamba said at the Leaders in Football conference held at Chelsea's Stamford Bridge stadium in London.
"If you look at the start of the season, the guys have not been playing particularly well -- the results have not been up to the standards we thought with the players we've got in the team.
"I was obviously devastated to see he was going but I am sure the club and the chairman will bring someone in to get promoted because we need to get promoted.
"In football you make changes and sometimes that's good, sometimes it's bad. We just have to wait and see how the club react.
"Football is results game and you get paid and picked if you play well. If you don't, you get out the team.
"For players it is the same as a manager. You stay in the job as long as the boys are performing for the team.
"I can understand exactly where the club came from, but at the end of the day he did a great job for the club and I am grateful to him."
He was coy when asked about his own future and said he was just enjoying some time away from the game.
"I have just been enjoying life, spending time with my family," Muamba said.
"I am writing a book at the moment, which will hopefully be out in November.
"I have been travelling as well but I never watch much football because I get really frustrated. As a professional, you get frustrated not being involved."
Asked about moving into management, he said: "Regarding coaching, I'm too impatient. I would like to be involved in football in some shape or form."