I read the book once and watched the series at least 3 times. What I think Mr Winters meant when he said he was no hero, was that there were countless men and officers around him during those horrific experiences that did exactly what he did. His story has been recorded for posterity. The others' stories are lost in the sands of time never to be recounted again.
The sadness is that we, the survivors, the beneficiaries of the actions of men like Mr. Winters do not appreciate the value of these stories anymore.
What frightens me nowadays as I look at myself, the people I see everyday, my colleagues and the people in the news and other media is that I don't see Dick Winters in them anymore.