In her retirement statement she said: "I do despair that the sport will never clean itself up when rewards of stealing are greater than riding clean."
But, although Armitstead understands why Cooke spoke out, she said on Tuesday that she did "not understand the benefit of bringing it up".
She added: "I just find it upsetting because the sport that I love, cycling, is clean now. My sport now is not that sport anymore.
"We shouldn't be adding fuel to the fire because for me, if I was a general member of the public and I saw someone in Nicole's position, at the top elite level of sport saying something like that, you're going to believe it."
When asked if she had ever been offered any drugs, Armitstead answered: "That's never happened to me, no."
Armitstead may not have enjoyed a smooth relationship with Cooke during her career, as the two also
battled to be lead rider
for Team GB in the Olympic road race, but the Yorkshire rider praised Cooke's "fantastic career".
"She has been so dominant for so many years but in the last season I could see she was not perhaps the person she was," concluded Armistead.
"I think it's good for her to retire and move on to something new."
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