Bournemouth have parted company with boss Paul Groves and assistant Shaun Brooks after winning just one of their 10 league games this season.
The Cherries, who are 20th in League One with only eight points, lost 3-1 to Crawley on Tuesday.
"Paul Groves and Shaun Brooks have asked me to express their thanks to the support they have received from the fans," said chairman Eddie Mitchell.
"We wish them well in the future, and who knows where that will take them."
Mitchell, who faced a fans' protest on Saturday following their defeat by Walsall and was hit on the head by a programme, added: "I would urge our supporters to recognise the time and effort that Paul and Shaun invested in the first team and their unwavering determination to produce an attractive brand of football.
"As chairman of AFC Bournemouth, I have personally recognised the direction in which they were trying to take the team in terms of tactics and style of play, and throughout their time in charge they have had my full support.
"However, I believe that luck has not been on their side during their short period at the helm.
"As we know, football is a results business, but most people will be unaware of the hard work and dedication that they put in behind the scenes to help this club move forward."
On Tuesday, Groves had vowed not to turn his back on the club, despite fans calling for him the resign.
He told BBC Radio Solent: "In football you don't quit. Never quit on the pitch, never quit off the pitch."
Groves was appointed permanent manager in May, after taking over as caretaker boss at the end of last season, following Lee Bradbury's sacking in March. He was given a two-year contract, but won just three out of 20 games as Bournemouth manager.
In September the club appointed former Tottenham boss Harry Redknapp in an advisory role at the club.
First-team coach Dennis Rofe could now take charge on Saturday, but it is understood that the club are working hard to bring in a caretaker manager for the weekend.