Australia won the fifth test at The Oval by an innings and 46 runs on Sunday to leave England as 3-2 winners of the series.
"We can't let this loss take the gloss off a special summer," a beaming Cook said before being presented with the Ashes urn.
"Credit to Australia and the character they showed to bounce back here. They have shown what a good team they are and to have beaten them three times is a credit to our guys.
"The fact we were underdogs before the series helped us. We were able to play with a bit of freedom and put them under pressure at crucial times.
"This has to be right up there in terms of my achievements and I am very proud of my team. I think we as a team have some amazing times ahead of us."
Cook admitted England had under-performed in the final test.
"It wasn't complacency but emotionally to come from such a high at Trent Bridge and be 100 percent on it was hard and we couldn't quite manage it," he said.
Joe Root was named England's player of the series after scoring 460 runs, including two centuries.
"Joe Root has been outstanding and led our batting, he has been our leading light and he thoroughly deserves to win man of the series," Cook said.
"Australia will be sitting there not quite believing that they've lost the series after playing as well as they did here.
"Are we near the peak? No we're not, we're nowhere near the finished article, but we've got a very exciting team and I genuinely believe there will be some really good times.
"Sport tests you in so many ways, but hearing the crowd now sends tingles down your spine."
(Editing by Mitch Phillips)
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