"Right now, it really hurts," Doolittle said. "But it doesn't do you any good, it doesn't do your team any good, to sit and mope and sulk and feel sorry for yourself."
The bearded closer's fourth blown save in 25 chances negated a stellar start by Jeff Samardzija and ended Oakland's two-year reign as AL West champion. The Los Angeles Angels clinched the division with a 5-0 win over Seattle and the loss by the A's.
Oakland dropped into a tie with Kansas City for the American League's top wild card. Seattle is two games behind the A's and Royals for the second and final berth.
"It's going to be a turning point one way or another," Doolittle said. "After the season's over, are we going to look back and point to tonight and be like, 'This is the game where finally the wheels came off for good,' or are we going to pick ourselves up, dust ourselves off, and talk about how resilient we are as a team and how we were able to overcome a game like this and still get it done?"
The answer remains to be seen.
Sam Fuld's single in the fifth drove in Oakland's only run. The A's stranded 10 runners and loaded the bases with no outs in the eighth only to come up empty.
Robbie Ross (3-6) got the final five outs for Texas, which has won five in a row.
"It's beautiful. I love it," interim Rangers manager Tim Bogar said.
Samardzija outpitched Derek Holland to put the A's in position to start turning around their late-season slide. Samardzija struck out 10 and allowed just four hits in eight innings.
As well as he pitched, though, it wasn't enough for the A's to overcome another underwhelming performance at the plate and a late flop by the bullpen.
Elvis Andrus singled and scored on Rougned Odor's double off Doolittle (1-4) to start the Rangers' rally. After Adrian Beltre was intentionally walked, Arencibia's 10th home run silenced the crowd of 17,530 at the Coliseum.
Doolittle was charged with five of the six runs. Oakland is 5-14 since Aug. 28.
"You look at our numbers and you say, how can this happen for this long a period based on what we did in the first half?" A's manager Bob Melvin said.
Holland continued his remarkable return for the Rangers after missing five months following offseason knee surgery. He gave up one run, four hits and three walks in 6 1/3 innings.
In four starts this season, Holland has allowed just three runs. His latest outing still wasn't enough to outlast Samardzija, who provided a much-needed performance on the mound after Oakland's sloppy 6-3 loss to Texas on Tuesday night.
Samardzija stranded a runner on second in the first, third and fifth -- the only threats he faced all night. He has allowed no runs in five of his starts with the Cubs and A's this season -- but hasn't won any of them.
"No time to pout. No time to feel sorry for yourself," Samardzija said. "That's just the way it goes."
Plate umpire Kerwin Danley took a foul tip from A's second baseman Nick Punto off his face mask in the fifth. Danley was replaced by second-base umpire Mark Ripperger to start the sixth, looking woozy as he staggered off the field.
Rangers: OF Shin-Soo Choo, already out for the season with an elbow injury, had surgery on his left ankle to remove torn cartilage and a small bone spur. He is in a walking boot and should start a running program in six to eight weeks.
Athletics: C Stephen Vogt (sprained left ankle) was intentionally walked as a pinch hitter in the eighth. He hadn't played since Sept. 3.
Rangers: RHP Nick Martinez (3-11, 4.93 ERA) starts Thursday's series finale. He's 2-5 with a 4.72 ERA in his past 10 starts.
Athletics: RHP Sonny Gray (13-8, 3.18) takes the mound for Oakland. He has allowed four earned runs in 15 innings over his past two starts.