The Robins suffered a comprehensive 4-0 defeat to Leicester City at Ashton Gate, their 16th loss in 26 games this season.
Director Jon Lansdown said in a statement: "This is a decision we felt we had to make for the good of the football club. Derek has been a pleasure to work with; he's disappointed but he understands the decision."
The statement continued: "We want to give ourselves the best possible chance of getting out of the situation we are currently in and we've got 20 games to do that."
- Sports & Recreation