Need 'thick skin' in NFL, says former Giants star

McConkey on bullying: Absolutely bizarre

Bigger players "tried to intimidate and bully me," said former New York Giants wide receiver Phil McConkey, calling the Miami Dolphins scandal one of the "most bizarre stories" he's seen in his decades of following professional football.

"To be in the locker room, you have to have very thick skin," McConkey, now an investment adviser, said on CNBC's "Squawk Box" on Monday—a day after suspended Dolphins offensive lineman Richie Incognito broke his silence.

In an interview with Fox Sports televised Sunday, Incognito said he regrets the racist and profane language he used with Jonathan Martin, but said it stemmed from a culture of locker room "brotherhood," not bullying.

(Related video: Beating a bully at work)

Richie Incognito #68 of the Miami Dolphins
Ron Elkman | Sports Imagery | Getty Images

Incognito is accused of bullying the second-year lineman, who left the team two weeks ago. Through his attorney, Martin said he could no longer stand the harassment.

Since all this came to light, stories have surfaced of Incognito's alleged bullying, going back to his college days.

While saying he'd never condone bullying, McConkey talked with CNBC about his personal experience as a player.

He said he had been small by NFL standards, and bigger teammates had "tried to intimidate and bully me to no end." He said he can't imagine being as big as the 6-foot-5, 312-pound Martin and "walking away from your team."

McConkey, a member of the Giants' Super Bowl-winning team in 1987, said, "It brings me back to one thing Bill Parcells—the legendary coach, Hall of Fame coach of the New York Giants—would always say, 'This game is not for the faint of heart.'"

In life after football, McConkey entered the financial services industry. He's now president of Academy Securities, a veteran-owned and veteran-staffed institution.

McConkey is a graduate of the U.S. Naval Academy and served five years in the Navy as an aviator and nuclear weapons transshipment pilot.

By CNBC's Matthew J. Belvedere. Follow him on Twitter @Matt_SquawkCNBC.