Playing what had been deemed a must-win game, the Coyotes blew a 2-1 lead and lost to the last-place Buffalo Sabres on Thursday night.
After the game, Doan was clearly agitated, calling the team's effort "embarrassing."
Phoenix got off to the second-best start in franchise history, but has struggled lately, falling to ninth in the Western Conference.
The loss to Buffalo was even more aggravating because it came two days after the Coyotes played perhaps their best game of the season, a 3-0 win over the Los Angeles Kings.
Phoenix has three games left before the Olympic break, all against teams still in the West playoff race: against Chicago and two against Dallas.