Democrats also lost a vote Wednesday on an amendment that would have given troops equal time when stationed stateside as when deployed to war zones.
"Well, we didn't make it today, but we're going to keep trying," Levin said Friday during a news conference.
He said Congress would keep "trying to pass a law ... which will require that there be a change of mission to more of a support role and that there be a goal, at a minimum, for the completion of that transition."
Levin said he and others would work to draft and share language aimed to pick up additional votes, "particularly Republicans." He said one possibility under consideration would be to change a binding date to complete the transition "into a date which is a goal for completing the transition."