Asiasi logged 23 of a possible 59 snaps on offense in Thursday's 24-3 loss to the Rams.
Meanwhile, fellow rookie tight end Dalton Keene was out there for 31 snaps, but neither player caught a pass Thursday. With Ryan Izzo (hamstring/hand/neck) on IR and Jordan Thomas having been a healthy scratch Week 14, both Asiasi -- who saw one target versus the Rams -- and Keene could be incorporated more in the Patriots offense down the stretch. Until that happens, however, neither player merits fantasy consideration.