Foster was inactive for the Texans' season-opening win over Indianapolis and carried only 10 times for 33 yards, sitting out the second half in Houston's Week 2 victory over the Dolphins when his hamstring tightened.
Tate ran for 82 yards on 19 carries in the loss. He had become the 11th player in league history to open his career with back-to-back 100-yard games, a list that includes Earl Campbell, Billy Sims, Marshall Faulk and Edgerrin James.
Despite Tate's fast start, Houston coach Gary Kubiak has said Foster will regain his starting role when he's fit enough to play.
"It's tough," Foster said Friday. "I think it's more mental than it is anything because like I said before, it's not something you can really push through. It's not something that you can play with at 100 percent, so you just got to be patient with it. It's just got to work that way."
Information from The Associated Press was used in this report.