Snee tore the labrum in his hip during his side's defeat to the Carolina Panthers and will require surgery to repair the damage, which will rule him out for six months.
He told the club's official website: "I've always been a guy that, by Friday, could suit up and play. I was kind of secretly hoping I'd wake up and things would feel differently, I would respond to the treatment and the medicine.
"It just didn't happen. It's frustrating. It's just a new situation for me. I've always been able to play through things.
"Sometimes things nobody knew about, things that I kept to myself. But I had to be honest with everyone, because it really got to the point where I was doing no good, to be honest."
The Giants are 0-4 going into week five of their season.