The 21-year-old departed the club for Southampton this week for a modest fee.
MacAnthony believes that top Premier League clubs may regret not moving in for Edwards.
In a club statement, he stated: "I am delighted for young Ronnie to fulfil his dream of playing in the Premier League at last.
"In doing so, fulfilling the promise made to him by the club in regards to not standing in his way on this move to Southampton.
"I believe under Russell Martin that he will flourish and become an England international in the coming years.
"Ronnie is another young talent we acquired from non-league and has been outstanding for us over the last four years and we wish him so much success as he becomes a Premier League player."
MacAnthony added: "I would like to say a special thanks to his family who have been outstanding to deal with during Ronnie's time with Posh.
"He is another player, like Ivan Toney, who many clubs in the Premier League will regret not signing due to him being with a League One club and who I have no doubt will one day move for £50 million to one of those very clubs."