The Giants' failure to reach the playoffs after winning the Super Bowl in 2012 has prompted a reshuffle of their roster, with Bradshaw and Carty joining the recently-released Michael Boley.
"I saw it coming because of the money," ESPN quotes Bradshaw as saying. "Everything is about money, I guess, so yes I was expecting it.
"I'm not discouraged at all. I'm just looking towards getting healthy and working with somebody else. That is all I can do."
Bradshaw was with the Giants for six seasons.