Start with the obvious criterion: TCU made it to their conference championship where they lost a close game to a team they had earlier beaten. Alabama couldn't even win its division.
Beyond that, I'll let USA Today's Dan Wolken make the case:
>>TCU has a better record against the top 25 (2-1 vs. 2-2). It has a better so-called “strength of record,” which measures how many games your opponents won. They had a common opponent in Texas, which TCU controlled from start to finish in a 17-10 win while Alabama had to mount a last-minute drive to win back in Week 2.
And finally, TCU’s overtime loss to a top-10 Kansas State team is better than Alabama’s overtime loss to a four-loss LSU team that got pounded by Georgia Saturday in the SEC championship. There’s also the matter of Alabama’s other loss, which would make them the first two-loss team ever included — a huge hurdle for a team that didn’t win its division.
It’s really not a close call. In a year of imperfect teams, TCU did what it needed to do and Alabama did not. Punishing the Horned Frogs for having to play a conference title game against a team it already had beaten earlier this season wouldn’t just be controversial — it would undermine all faith in what the Playoff is supposed to value.<<