The England and Wales Cricket Board will name a new head coach next month, but Anderson believes that more players need to take responsibility to help whoever is given control of the team.
"As important as a head coach is, I feel it's the players that have to try and turn things round," the 31-year-old bowler wrote on his official website.
"I honestly believe the group of players that are selected have to take responsibility to try and get the team out of the trough we find ourselves in.
"A successful team is not led by one man. The captain is also important, of course, but a successful team has a group of leaders within the team. We will need a nucleus of four or five leaders who can drive the team in the right direction."
England take on Sri Lanka and India in all formats this summer.