The OPEN question is who is our 3rd RB. Belichick answered in BUFF by giving only two reps to Barner. Patterson is our 3rd RB.
I interpret that differently.
Aside from his TD, White had arguably his worst rushing performance of the season against the Bills - 1.88 ypc on 8 carries. I'd guess that the Pats knew in advance that none of their RBs was likely to have a particularly spectacular rushing performance last night (even Michel). So, they went with White and Patterson for their versatility (Barner isn't yet a reliable passing target), and then used Patterson experimentally as a runner out of the backfield, partly as a bit of trickeration that they hoped would gain some yards (it did) and allow for some misdirection later (it did).
I don't think that any of that was a reflection of the coaches' overall regard for Barner and his capabilities, as much as it was the specific game situation.
If there's a hierarchy, I'd guess that Michel (when healthy) is the #1 rusher, White is #2 now (and possibly #2b when Burkhead returns from IR).
Barner is the (active-most-games) #3, after Michel is back, and Patterson is the (always-active) #4. When Burkhead returns, Barner becomes the (mostly inactive) bench depth #4, and Patterson is the (always active) #5 (similar to Bolden in that regard).
Of course, it's possible that, once Burkhead is back and contributing (wk-13 at the earliest), the Pats may decide that having a never-active RB as bench depth is a luxury they can't afford, roster-spot wise, and let Barner go.
In the meantime, I don't see much point in sweating about getting an upgrade to Barner. It's halfway through the season already, Barner is already trained in the system, and Burkhead's reinforcement effect is in the pipeline (as far as we know).
If the Pats find out (soon) that Burkhead isn't coming back this season after all, THEN (maybe) it's appropriate to put some effort into finding an upgrade for Barner.