It feels really weird to even consider the question of who to blame here. They went into a game massively outgunned, had a tragedy strike a key skill-position player not long before game time, took advantage of opponents' mistakes (see e.g. pick-6), and had a very realistic chance to steal the game on the final play. Honestly, the end of the game almost felt like partial karmic retribution for the Malcolm Butler play, it was such a reversal. As the game ended, the thought that went through my head was "well, I can't say they let me down".
If there's one frustration I have, it's not calling their last timeout after the Edelman play that took them to the 16 yl with 0:36 remaining. From there, even if Harry gets downed at the 1 on the next play, you can hustle up to the line, run a pass play, and if incomplete then you have time to run another one. Maybe two. Instead, they let the clock run, and the Harry play ended with 0:03 on the clock.
That said, if there's one coach in the league who is above reproach on clock / timeout management - particularly against Seattle! - it's Belichick. So I'm choosing to believe he did it to prevent substitutions or something, rather than a belief that there was no tactical difference for him in the number of plays he'd get to run.