Parker, who was on the field for all 57 snaps on offense in Sunday's 20-7 loss to Miami, caught one of his two targets for nine yards in the contest, Mike Reiss of ESPN.com reports.
From a fantasy perspective, the most encouraging thing about Parker's regular-season debut was his workload, as the 2015 first-rounder and Jakobi Meyers (50 snaps) were the Patriots' busiest wideouts Week 1, ahead of Nelson Agholor (33 snaps) and Kendrick Bourne (two snaps). While Parker no doubt will have better weeks production-wise, he'll profile as a speculative fantasy option until he sees increased target volume in New England's offense.