EAST RUTHERFORD, N. J. -- By nature, coaches are teachers and their players are pupils. So when a pupil doesn't succeed, there is naturally disappointment on the part of the coaches.

That's how Giants head coach Tom Coughlin is feeling these days after having not one but two members of his defensive secondary -- safety Will Hill and cornerback Jayron Hosley -- handed league-imposed suspensions related to their failure to adhere to the NFL's policy on substance abuse.

"It's disappointing as heck, as you can imagine," Coughlin said of the circumstances, "but we go on."

Unlike Hosley, who is fighting for a roster spot, Hill, who was written in ink to be a starter, is no longer with the Giants after being waived him on Monday.

Coughlin said Hill's behavior -- the safety received three suspensions in as many years -- really left the club with no choice.

"When you run a business, you have to be able to rely and depend on people to be there when you need them to perform their duties," Coughlin said.

"If this is your job and you're willing to jeopardize your job for some other reason, than perhaps you don't have your mind and priorities where they should be in the first place."

Safety Antrel Rolle, a leader on the defense, also expressed disappointment in both Hill and Hosley.

"They know if they're going to be tested and when they're going to be tested. It's too easy to do right to keep doing wrong," he said. "That's something we don't need around here -- fans asking me on Twitter what is up with the secondary. It's a bad reflection; it doesn't look good."

Hosley, who received his first strike under the league's policy, a violation that will keep him out of the first four games of the season, offered a heart-felt apology to everyone from team ownership right down to his teammates and the fans for his indiscretion.

"My coaches have expectations of me and I have expectations for myself," he said. "We all make mistakes, but right now I'm just focusing on football and surrounding myself with good people -- my family, who's always been there for me."

Hosley said he regrets causing a distraction for the team. However, he's looking forward to having the opportunity to put this situation behind him and showing the Giants that he can indeed be counted on in the future.

"It's not about the mistake that was made; it's about how you overcome it and how you move forward and how you approach the situation," he said. "You can't dwell on the past; you have to move on.

"I dealt with the issues I had to deal with when it initially happened. It's not about what I'm doing outside of football; it's about football right now."

NOTES: WR Odell Beckham Jr, the Giants' first-round pick, was held out of practice because of some hamstring tightness. Beckham told reporters that his ailment "wasn't' a big deal." However, head coach Tom Coughlin said the rookie could miss a few days as a precautionary. ... LB Spencer Paysinger said he has been working at the strong-side spot, the role previously held by Keith Rivers, who signed with Buffalo as a free agent.