The former Chelsea midfielder insists all that could change though if they continue to progress at World Cup 2010, with Germany in their last 16 tie next on the agenda for the Three Lions.
"We [England players] don't like to be called the 'Golden Generation'. That was put upon us. We don't like it because we've not won anything,” Cole told BBC Sport.
"We want to win something. Then people can rightly call us that. I remember the Portugal team who were called the same and they never won anything either."
After an improved performance in their final Group C game against Slovenia, Cole feels that England are ready to face the daunting task of defeating their rivals in Bloemfontein on Sunday afternoon.
"I thought it was an excellent performance against Slovenia and we can't wait to get to grips with Germany," he added.
"I think we can do it this time. I've never felt it like this before in other tournaments. You always think you can do it but this time I think it's our time and we can do it if the country believes.”
Like many others in the England squad, Cole’s first experience of a World Cup came as a boy watching the tournament in 1990.
"The history between the two countries is immense and the 1990 World Cup was the first tournament I watched," he said.
"I can remember when Gazza [Paul Gascoigne] got booked and we lost on penalties to Germany in the semi-finals."
Cole has never taken a penalty in his 12-year career as a professional. Despite this handicap though, he is ready to put himself forward should the situation arise.
"I've never taken a professional penalty because when I was at West Ham [United] Paolo Di Canio took them," he concluded.
"Frank Lampard takes them at Chelsea and David Beckham always did for England - but that's not to say I wouldn't take one.
"I'm hoping there'll be no surprise and they'll fall to the [Steven] Gerrards, [Frank] Lampards and [Wayne] Rooneys but if the manager asks me, I'll be there.
"It takes more of a man to step up and take one rather than shy away.”
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