Probably the same way anyone else involved in an accident lives with it. Simply acknowledging that events were beyond his personal control. You folks wanting to hang stewart without even knowing the facts act like nobody has ever died before.
What hasn't been said in any of the threads that I read is that knowing that a car flipped and crashed (not just crashed), and that a yellow flag was out, the drivers should have been expecting service vehicles to be entering the track to remove the car and should have been on the lookout for it. That means slowing down, being aware of the goings on at the track entry point, and being aware of the goings on at the crash site.
I put an extra burden on a veteran like Stewart to role model the safety culture of NASCAR.
-PJ