All three played key roles in helping the Giants win the Super Bowl just over a year ago. And Bradshaw helped them win two Super Bowls.
"You are always surprised when you lose guys who have been very integral in what we have done over the years," Tuck said at the Founders Dinner gala at Cipriani Wall Street on Tuesday night. "But you also understand the business side of it, and at times like this you wish those guys wouldn't have been part of it, but it happened."
Tuck has seen Jerry Reese and his staff make painful bottom-line decisions before, and he has seen the results.
"From what I understand in conversations I have had with guys, it was a money issue, you got to cut cap," Tuck said. "Those guys (management) have done a great job over the years of building a team that can be successful and I don't see why we can't trust in the fact that they know what they are doing up there.
"Those decisions aren't easy decisions," Tuck continued. "I am sure Jerry and everybody up there had some tough times and some tough conversations about them. They felt as though it needed to happen and they went forward with it."
The Giants reportedly cleared $13.75 million to get below the salary cap with those three moves. The Giants likely still have to clear more room to sign some free agents like tackle Will Beatty, tight end Martellus Bennett and left guard Kevin Boothe.
So the Giants may very well have a few more tough moves regarding some longtime veterans. Tuck, who is entering the final year of his contract worth $4.5 million in base salary, is not expected to go anywhere. He said the Giants have not approached him about his contract.
As for how the Giants will replace three key veteran personalities and leaders on the team, Tuck said the they will find a way.
"Anytime a guy was hurt or a guy is leaving or cut, there is always opportunity for somebody else," Tuck said. "We got guys on this team that need to step up and play better and do whatever role is needed from the coaching staff to have a successful football team. As OTAs and training camp comes in, we will figure all that out."
"Some people speculate that we might have a chance to get some of them later on," Tuck added of Canty, Boley and Bradshaw. "But either way, you are just wishing them -- wherever they end up -- success, and hopefully they continue with their great careers."