Probably because Washington is the worst tactician in baseball and they missed the playoffs by one game for the second straight year. This game pretty much summed up his tenure with Texas: bat AJ Pierzynski 5th against a lefty, pulled his starter who was rolling after 85 pitches and put in a reliever he's used for 4 consecutive days who then promptly gave up a run, had a player bunt at the worst moment.
None of that mattered, because David Price was dealing. It was absolutely the right call to pull Perez there with Longoria coming up - and Ogando had been pitching well. Their other relievers had pitched 4 days in a row leading up to the game and he didn't want to stretch them past 1 inning each.
He isn't going to be fired - the reason the Rangers are where they are were from things Washington has no control over.
1) Not replacing Hamilton/Napoli/Young (not saying there were any good options out there, they definitely tried to get Stanton, etc.), this was the 2nd worst offensive club in 40 years of Ranger history. Yu Darvish lost four 1-0 games.
2) 2 of the 5 starting pitchers (Colby Lewis, Matt Harrison) lost for the year and a 3rd (Alexei Ogando) also out for huge swaths of the year. Guys they brought up, Grimm/Tepesch, did step up early in the year vs. weaker teams and Martin Perez has definitely proven he can be a #3 starter like he was projected to be.
3) Nelson Cruz, their best slugger, gets suspended for 50 games. Rangers offense didn't go into a ditch immediately because they got to play a weak part of the schedule and Beltre was carrying them - but as soon as it toughened up in September the offense flatlined and they lost 15 of 20 before winning their last 7 against Astros/Angels just to get into a tiebreaker.
4) Matt Garza sucked after leaving the Cubs
That they still got to 91 wins with one of the worst offenses, basically on the back of 2 starters and a great bullpen, is pretty amazing.