"What they have to work out is how they are going to get some pride back in the team,'' Boycott said in a column in The West Australian newspaper.
"They cannot do that unless they bat with more common sense and stop gifting wickets away.''
Boycott said Cook appeared frustrated and worn down. Australia's bowlers had dried up his scoring zones.
"Australia have worked Alastair out,'' Boycott said. "They give him nothing to score off his legs or hip and they are winning the battle.''
The plain-speaking Boycott could barely contain his anger at Cook's second-innings dismissal.
"Here was our captain, who is supposed to set the tone, hooking Mitchell Johnson down fine leg's throat in the second over of the day which shows his brain is scrambled,'' Boycott said.
"We have some serious problems.''
Boycott said half of England's dismissals had come from bad shots and he took aim at Kevin Pietersen for chipping catches to mid-wicket three times despite an obvious plan to claim him there.
As Cook pointed out in his post-match news conference in Adelaide on Monday, Pietersen showed more restraint in his second-innings 53.
However Boycott added: "We cannot seem to find a batsman who can bat properly in every innings and not give their wicket away.''
-AAP