"We entered this season with tremendous optimism based on the pedigree of both Darije Kalezic and Rado Vidosic - both title winners, both excellent football thinkers."
Vidosic resigned following a 1-0 loss to the Glory in Perth on Saturday.
Doubling the Phoenix woes is that his son, who has played 23 matches for the Socceroos, will also exit.
Dario Vidosic scored four goals in 10 appearances and had largely impressed in the wake of knee surgery in the off-season.
The 30-year-old suffered a knee injury against the Glory and his immediate fitness - and playing future - are uncertain.
Dome said playing and coaching replacements will be sought when the January transfer window opens.
He tried to paint the departures in a positive light.
"It's an outcome that enables the club to move forward and focus upon turning around a disappointing run of results.
"We've put tremendous work this season into progressing the culture at this football club and the players and staff have bought into this."
The Phoenix host league leaders Sydney FC in Wellington on Saturday.