The 31-year-old will look to find another club after the arrival of Amari Morgan-Smith from York City.
Former Wolves star scored four goals in seven games for the Bucks but Edwards knows it wasn’t possible to keep them both following his signing on transfer deadline day.
Edwards told the Shropshire Star: "The budget, that's all that it is. We can't keep everyone. A lot of our players are on contracts and Sylvan wasn't one of them.
"We made a couple of signings last week and we are looking to make a couple more, to strengthen the squad.
"That's all it is. It was a difficult decision, but one I had to make in the best interest of the football club."
"His attitude has been first class with us. I wish him well."