The hosts completed a 150-run win in Perth on the final afternoon - despite a maiden century from Ben Stokes - to go 3-0 up in the five match series and claim the urn for the first time since they inflicted a whitewash on Andrew Flintoff's men four series ago.
Cook said: "We've been outskilled in all aspects. It's hard to say that as a player but that's the honest truth.
"We've got to keep looking at ourselves, keep doing what we can do which is work as hard as we can to turn things around."
Cook insisted his side had not been taken by surprise by Australia.
"We knew what a good side they were in England," he said. "Any side coming to Australia, you have to be at the top of your game to compete. We haven't been there.
"They've been ruthless - ruthless in never letting us back in any game when they got ahead of us.
"But there's a lot of talent in the dressing room. Everyone's hurting now, it's an incredibly tough place to be. That happens in sport - there's a winner and a loser and at the moment we're in the losing dressing room and it hurts.
"All we can do is work as hard as we can on our games and come out on Boxing Day and try and put in a better performance."
Stokes' 120 in 353 all out was at least a crumb of comfort to England.
Cook said: "It was a fantastic innings - full of character on a tough wicket with those cracks, it's always daunting to see them. He put them out of his head and I thought it was an outstanding hundred.
"You never know in sport. That partnership was just starting to build. But, as always, just when we've got a partnership going we haven't managed to continue."
Cook admitted he was bracing himself for an inevitable inquest into how England, who won the Ashes 3-0 on home soil in the summer, had surrendered them so tamely after the opening three Tests Down Under.
Cook told BBC Radio Five Live: "I'm sure they'll be a lot of inquests. There always are when you lose.
"It is a tough dressing room to be in. We haven't had enough people in form and we have been punished for it.
"They just outplayed us. We haven't managed to score enough runs and whenever they needed a partnership they got it.
"There is always a balance between risk and reward and our shot selection has let us down."
Looking ahead to the final two Tests in Melbourne and Sydney, Cook was reluctant to talk about any changes to the England side in the wake of the Ashes defeat.
He added: "We've got to go there and try to win the games.
"It is very early to say what we do with the side. There are always calls for change when you lose. We have the players to do it - it's about delivery."