The 29-year-old made a late hit on Talib on the sideline after the cornerback attempted to run back an intercepted pass from Geno Smith in New England's 13-10 win over the Jets.
"I made the tackle," Mangold told The Star-Ledger. "He was along the sideline. I obviously could not play defense in this league because I thought he was still in bounds, so I tried to make a tackle.
"He got heated about it. I was a little surprised by that. I figured he'd have a little bit more poise. But it's obviously an intense game, intense rivalry and tempers flare."
Mangold's fellow offensive lineman D'Brickashaw Ferguson and Willie Colon were ejected from the game in a melee that followed the incident.