The tourists trail the current series 2-0 Down Under following a 218-run defeat to Australia at the Adelaide Oval on Monday, with Cook being dismissed for one in the second innings.
"Australia have worked Alastair out," Boycott said in a column for the West Australian newspaper. "They give him nothing to score off his legs or hip and they are winning the battle.
"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. We have some serious problems.
"What they have to work out is how they are going to get some pride back in the team. They cannot do that unless they bat with more common sense and stop gifting wickets away."
Australia can reclaim The Ashes and end a run of three straight series losses to England with another win in the third Test, which gets underway at The WACA in Perth on Friday.