Tomlinson was on the field for 38 of the Patriots' 82 snaps on offense in Monday's 33-0 win over the Jets.
Tomlinson, who was making his debut with the Patriots, worked behind Ben Watson on Monday, en route to hauling in his only target for one yard. Looking ahead, Tomlinson's fantasy upside is modest, while his snap counts in the coming weeks figure to hinge on the availability of fellow tight ends Ryan Izzo (concussion) and Matt LaCosse (knee).