The anguish was much deeper for Bush, who suffered his third blown save in his last five opportunities when he allowed a game-tying home run to Brett Gardner in the ninth and a game-winning single to Ronald Torreyes in the 10th.
"I am trying the best I can," Bush said. "It's very difficult. I feel the weight of these losses. It's very tough mentally and physically. I'm doing what I can. It's not going my way, but I am going to keep grinding through it."
Darvish, who was brilliant for seven innings, said he should be fine for his next start against the Indians on Wednesday.
"It's not that I am feeling any pain, but it started in the fourth inning," Darvish said. "I started feeling tightness. I didn't want to push it and affect my next outing."
Darvish allowed just two hits, did not walk a batter and struck out 10, including the last four batters he faced.
This was only the ninth time in 116 career starts that Darvish did not walk a batter. It's also the fewest hits he has allowed without walking a batter since coming within one out of a perfect game against the Astros on April 2, 2013.
He left with the game scoreless. The Rangers pushed across the go-ahead run in the top of the ninth, but Bush couldn't close it out. Gardner tied the score when he hit a one-out home run over the right-field wall.
Bush got out of that inning on just 15 pitches, and the Rangers decided to send him back out for the 10th in a tie game. Manager Jeff Banister, who had already used Tanner Scheppers in the eighth, said Keone Kela, Alex Claudio and Jose Leclerc were all unavailable because of their recent workload.
"Matt was still fresh," Banister said. "We felt if we could get through that inning, we had a chance."