Cook was a member of the team that won the Ashes back in 2009, England's best batsman when they retained them in Australia in 2010-11 and captained the side to a dominant 3-0 home triumph earlier this year.
His team's batting woes have been reflected in his own displays in Australia, though, and emphatic defeats in Brisbane, Adelaide and at the WACA on Tuesday saw the urn return Down Under.
"The dressing room is hurting like hell. It's a tough place to be. We've had plenty of success and this is the other end of it. It's not pleasant," he told reporters.
"In sport, if you turn up and aren't good enough, you're going to get found out. We haven't been good enough, that's the reason we lost.
"I'll never be embarrassed for the way we go about things and the effort the lads put in. It's a hard thing to say when you've been beaten and you deserve to get beaten. It's never good as a sportsman to admit it, but we have."
Cook said losing top order batsman Jonathan Trott, who returned to England after the Brisbane defeat to deal with some mental health issues, had been a "tough moment" for the team.
"When you watch your mate, who you've had a lot of good times with, and some tough times as well, when you watch him go through what he went through, and try to keep it out of the public as well, was tough," he said.
"When you lose a player of his experience and quality you are going to lose something. But I think we'd be looking into excuses if we start blaming that for one of the reasons why we lost this series."
Cook, who is averaging 25.66 in this series, was happier to give credit to Australia and rejected suggestions the hosts had triumphed courtesy of greater effort and desire.
"I think it's the first thing you do when you lose - people look at the hunger and the desire," he said.
"I can honestly say in our dressing room, both are there. We just haven't had the skills to match it.
"Sport is not about trying at all - it's about delivering. We know we tried as hard as we could and we haven't delivered. We have to give credit to Australia.
"The way they fought back from what happened in England to here. They've done an outstanding job behind the scenes and a lot of their players have had very good series."
Cook said he thought he and coach Andy Flower, whose rolling contract is up for renewal at the end of the tour, were still the right men to lead England forward.
He got some support from his opposite number Michael Clarke, who knows only too well what it is like being under pressure after leading Australia to a 4-0 defeat in India and that 3-0 Ashes loss in England this year.
"From my personal experience, I believe Alastair Cook is a wonderful player and a very good captain," said Clarke.
"They outplayed us two months ago, in the UK. I don't think it's fair to judge his career or his captaincy on three test matches in Australia."
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