Nelsen, who took charge of the MLS franchise in January last year, and most of his coaching staff were relieved of their duties following Saturday's 3-0 loss to the New England Revolution.
The defeat extended Toronto's winless run to three games, and left Nelsen and Bezbatchenko at loggerheads with each other.
Nelsen responded angrily to Bezbatchenko's challenge of the team during his post-match conference on Saturday, with the former New Zealand international criticising the general manager for putting his players under unnecessary pressure.
His comments appear to have been the tipping point for Toronto, who moved swiftly to replace Nelsen, with Greg Vanney promoted from the club's academy on a full-time basis.
"Over the past 13 matches we've won three games," Bezbatchenko said on Sunday.
"Thinking about our locker room and knowing our guys, I know we can get more out of our guys. We've lacked purpose offensively and defensively.
"I believe in the group of players we have here at Toronto FC. This is a group that we know is capable of winning and it’s our job to put them in a position to be successful.
"Our recent results have fallen below our expectations and a change was needed.
"Greg is a person that possesses all the qualities that align with our vision for Toronto FC. I'd like to thank Ryan and the coaches for their efforts and wish them well in their future endeavours."
Nelsen's departure may also lead to Jermain Defoe's exit, with the former Tottenham striker reportedly in talks to return to the Premier League.
