Manning told KRIV-TV in Houston that despite his release, there's "no bad blood" between himself and the Texans.
Last week, the Texans asked Manning to restructure his contract, a move that would reduce his salary and cap numbers and allow him to stay with the team.
Manning's agent told KRIV-TV last week that the safety was willing to take a pay cut but not to the level at which the Texans were requesting.
Manning, who turns 32 in August, was scheduled to make a base salary of $4.5 million this season, with a cap number of $6 million, in the final year of his contract.
"I'm dealing with it great," Manning told KRIV-TV of his release. "Both parties agreed to disagree. It's nothing personal. I'm really not upset at all."
He initially signed with the Texans before the 2011 season, a four-year deal worth $5 million a year with a total guarantee of $9 million.
Last season, Manning started six games before he suffered a severe knee injury after hyperextending it during the Texans 38-13 loss to the Rams on Oct. 13. He is expected to be ready for the 2014 season.
The Texans signed safety Chris Clemons last week. The two-year deal is worth $2.7 million and includes $450,000 in guaranteed money, sources said.
Clemons' salary with the Texans was similar to the salary offered to Manning in his pay cut.
ESPN NFL Insider Adam Schefter and ESPN.com Texans reporter Tania Ganguli contributed to this report.