Agnone said that Strahan struggled deciding whether he could give 100 percent mentally.
"In the end, he felt he could not get back to where he was," Agnone said.
The first report of the news was provided by FoxSports.com, which contacted Strahan in Greece where he was vacationing.
"This has been one of the toughest nights of my life," Strahan told FoxSports.com. "But after long deliberation and throwing around a million scenarios in my head for the past day, I think it's just best if I stay retired."
Giants general manager Jerry Reese has asked the 36-year-old Strahan to reconsider his retirement on Monday, just 48 hours after the Super Bowl champions lost Pro Bowl defensive end Osi Umenyiora for the season to a knee injury in the preseason game against the New York Jets.
Strahan needed just about a day to turn down an offer to return for a 16th season with what could have been an $8 million contract.
"I really love my life now," Strahan said. "It's great having nobody put a finger on me. You really put yourself through an awful lot in this league, more than people realize.
Agnone said money was never an issue.
"We know the parameters of the contract and the Giants would have been generous," Agnone said.
Reese did not seem surprised by the decision.
"We knew it was a long shot, but we owed it to ourselves to exhaust the possibility," Reese said late Tuesday evening. "We appreciate Michael even considering ending his retirement. He has a new career in front of him and we wish him nothing but the best. As we all said when he announced his retirement, Michael was and is a great Giant."
The Giants moved Mathias Kiwanuka from linebacker to defensive end on Monday to take over for Umenyiora, who had successful knee surgery on Tuesday morning and was placed on season-ending injured reserve.
The move will not be a major one for Kiwanuka. He was drafted in the first round in 2006 as a defensive end and started nine games as a rookie. He also lined up as a defensive end in third-down situations last season.
"There is a reason he went in the first round obviously," middle linebacker Antonio Pierce said. "The guy, he is playing behind Strahan and Osi, and then we moved him to linebacker, so obviously he is one of our top players on the team and he is going to show that he is a top defensive end in the league."
Pierce also said the team was ready to move on with or without Strahan, the team's sacks leader who retired in June, four months after earning his first title ring.
"We know we are a confident team and we are a playoff-capable team and we have to go out and perform like it," Pierce said before Strahan announced his decision. "The reason we took the (underdog) role last year was because everybody said it, and we just went with it. We're not thinking like that this year. We do have a chip on our shoulders and it grows more and more when somebody gives us something to feed off of."
What's bugging them now is the belief by some that they don't have the players to get the job done with Umenyiora out.
Pierce never thought that money would be the deciding issue for Strahan.
"The only reason he will come back is if he wants to play," Pierce said.
Obviously, Strahan did not want to play.
Strahan has signed a $2 million deal to work for Fox Sports on its NFL pregame show on Sundays.
