Before the game, he had some hope of keeping his job, since the two losses previous to us, were close games against good teams. He was probably counting on the game being a shootout.
I'm pretty sure that the powers-that-be at Arkansas told him "win or else" probably setting the bar at not having a losing season.
With the remaining schedule, there's no way he'd be able to pull out a winning season, or even get to .500, barring some divine miracle.
At first glance, someone may think that they'll have a chance against Auburn, Mississippi State, and Missouri, but it's not looking good.
Auburn barely lost to what are now two top 10 teams and Mississippi State lost a close OT game to Tennessee. At this point, if Arkansas could get their offense going again, they could take one of these two with a lot of help from Lady Luck. This is possible, since Petrino can work some magic when it comes to the offense.
Missouri, even with its 5-0 start, will be exposed in the 2nd half of the season. I think Arkansas has a fair chance at winning.
For the rest of the games, they're going to lose, barring some meltdown by the stronger SEC teams.
The Razorbacks' remaining schedule:
@Tennessee
Texas A&M
Auburn
Mississippi State
@ LSU
@ Texas
Missouri