Burke did what he thought was best for the team. He go fired because the new management didn't like his approach. He has left a pretty bad team with little numbers of good prospects. Its not all on him though.
They've had lots of underachieving players, bad drafting partly because of poor scouting, and Toronto, as a market, isn't a place most players would like to go.
Edmonton started their rebuild around the same time but they had the advantage of having a market players want to go to along with great drafting. Toronto has been on the bottom for too long but they are never low enough to get good prospects. That, and giving away those couple firsts to Boston has left them depleted.
Burke simply isn't in his environment in Toronto. He did do a poor job, but it was not all on him.