The Trotters have struggled since relegation to the second tier and lie 18th after collecting a mere 11 points from 10 matches. Such form saw Coyle sacked on Tuesday after nearly three years at the Reebok Stadium helm - a move Muamba was sad to see.
The midfielder was forced to retire from football after suffering a cardiac arrest while playing for Bolton in March, with Coyle praised for his support in the aftermath. 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. "If you look at the start of the season, the guys have not been playing particularly well and 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."