Warnock has brought his own backroom team with him and Symons did not figure in the plans of the former Sheffield United manager.
Mick Jones is the new assistant manager, with former England international Keith Curle taking on first team coaching responsibilities.
Symons had been with the club since 2001 and had been keen to remain on the coaching staff.
When asked in the wake of Peter Taylor's departure whether he wanted to stay with the club, he told the Croydon Guardian, "Very much so - that's what I hope would happen, but you never know.
"I've been here for seven years now - this is my club now and I've got genuine affection for the place."
However, it was not to be and the Eagles now look to the future with an entirely new back room team.