There are 3 things that have let England down in this series only in my opinion of course.
1. Cook's poor captaincy ( tactical, field positioning, bowling changes )
2. Batsmen's lack of commitment
3. Anderson's poor performance with the ball ( don't want to hear "oh he is tired, worn out". He doesn't look at all interested and has no passion )
Cook should stay captain simply because their isn't anyone good enough to take over. He needs to sit back and look at his mistakes and talk to who ever he needs to to help correct these mistakes.
They have the batsmen to win but they need to work hard, find the commitment and just bat as long as they can.
Drop Anderson to give him a reality check... He isn't indispensable.