I can't say it's unfair. Parker has gotten the MVP chants for the last few months. He's gotten a lot of acclaim. So if the Spurs come up short, it only makes sense for your "best" player to get the brunt of the criticism.
For the record, asking Parker to be the best player on a championship team was always a tall task. Coming into this season, I would have laughed at the idea. I've spent more time defending Parker than anyone I know but still, best player on a championship team is asking a whole lot.
In the big picture, Parker has given it a great shot. He's brought the Spurs closer than I would have imagined he could coming into this season. But if it turns out he's not good enough, it won't exactly be shocking.
All that said, I'd love nothing more for Parker to answer with a 30-10er in Game 6 while leading the Spurs to victory.