Incognito said Martin "never showed signs that football was getting to him, [or] that the locker room was getting to him."
"As a leader, as his best friend on the team, that's what has me miffed," he said. "I never saw this coming."
Martin has since left the team and reportedly checked himself into a hospital last week seeking treatment for emotional distress. He was spotted leaving his parents' Los Angeles home Thursday.
Dolphins' players have defended Incognito and praised him as a loyal teammate with leadership skills. Teammates have been less passionate in their support of Martin, saying he and Incognito behaved like best friends.
"They did a lot of stuff together," tackle Tyson Clabo said. "So if he had a problem with the way he was treating him, he had a funny way of showing it."
Quarterback Ryan Tannehill said, "If you had asked Jon Martin a week before who his best friend on the team was, he would have said Richie Incognito.
"The first guy to stand up for Jonathan when anything went down on the field, any kind of tussle, Richie was the first guy there. When they wanted to hang out outside of football, who was together? Richie and Jonathan," he added.