"It is what it is. That is the life of the business," Brown said, confirming his release to ESPN's Josina Anderson.
The Texans also released running back Dennis Johnson on Monday.
To replace the two running backs, Houston agreed to deals with veteran tailback Ronnie Brown, who spent the past two seasons with the San Diego Chargers, and William Powell, who last played with the Arizona Cardinals in 2012.
Both Ronnie Brown and Powell were at practice with the Texans on Tuesday.
When asked what happened to prompt his release, Brown said: "I have no idea."
Foster has missed most of training camp with calf and hamstring injuries that might be related to back surgery he had last season.
Brown, 27, rushed for 492 yards and scored three touchdowns last season with the New York Giants.
The Associated Press contributed to this report.