Think the Cowboys lost this one when they started the season 3-5. Look at the way the divisional games played out. The Colts and Chargers both were smoked, and their quarterbacks -- very good quarterbacks -- looked awful. Even the Eagles, after having scored two quick touchdowns, never scored again. The higher seeds won all four games and dominated three of them (though the Cowboys game was close on the scoreboard).
The Cowboys looked like a team that played a tough playoff game and traveled to the West Coast for a second game against a rested opponent. The Chargers looked like a West Coast team that made back-to-back trips east. The Colts looked like a team that played one high pressure game after another, after a slow start to the season, and simply ran out of gas. The same could be said for the Cowboys.
The more parity evens the talent pool, the more difficult it is for teams to overcome fatigue and spent emotion. The Rams were better than the Cowboys, but the Rams OL was not better than the Dallas DL to that level of domination. The Cowboys looked like a tired, beaten up team. I think that's what they were.
I don't think it's a coincidence that Wild Card teams have been less successful in the divisional round than they were in the past. Rather I think the first round byes have become more valuable.