Parker (41) expressed his “not surprise” at the defeat and said that the squad was “ill-equipped at this level.”
Owner Maxim Demin said, “We must be unified in our approach to managing the club sustainably if we are to maintain improving as a team and a club as a whole.
“We must also demonstrate respect for and believe in one another.”
Demin continued: “We won’t deviate from the strategy that has helped this team achieve such great success in previous years. We will start looking for a new head coach right now.”
After winning their first game, Bournemouth suffered their third consecutive league loss after the humiliation by Liverpool.
The squad will be led pro-tempore by Gary O’Neil, with Tommy Elphick and Shaun Cooper on his side.