It won't be easy, though, with 13 of the final 21 games on the road, including series at Detroit, Oakland, Minnesota and Seattle.
Still, Washington pointed to the Rangers' record against American League West rivals to show his team's improvement.
"We were 6-15, and now look at us [at 22-24]... hmmm," Washington said.
The last time the Rangers finished .500 or better was in 2004, with an 89-73 record.
Kason Gabbard will pitch on Thursday against Oakland, if he's healthy.
Kameron Loe, who is battling right elbow soreness, is scheduled to start on Saturday, if he's healthy. Loe is progressing "slowly" though.
"We'll see how it feels," Loe said. "I want to get back and throw, but if we decide to shut me down [for the rest of the season], it's not the worst-case scenario."
Luis Mendoza was "sore" on Sunday, after being struck in the knee during Saturday's game. He is the No. 2 option to start on Saturday, if Loe is unavailable.
Brandon McCarthy, on the disabled list with a stress fracture in his right shoulder blade, will start the first game of Tuesday's doubleheader against Detroit. He will be limited to two innings and 35-40 pitches.
"I just want to get my feel back and keep working," McCarthy said. "I want to see a high percentage of my pitches for strikes."
If Loe and Mendoza are unavailable on Saturday, Washington said the team could have McCarthy pitch three innings in a piggyback start.
McCarthy said his offspeed pitches -- a curveball and a changeup -- have improved since going on the DL. His fastball was not affected by his shoulder injury.
Instead of the typical Rangers jerseys hanging on the lockers, several players showcased their football loyalties on Sunday. Well, it was more their fantasy football loyalties. Here's a look at the jerseys around the clubhouse:
Michael Young: Bengals' Carson Palmer
Hank Blalock: Chargers' LaDainian Tomlinson
Frank Catalanotto: Jets' Jonathan Vilma
Ian Kinsler: Cardinals' Matt Leinart
Jamey Wright: Cowboys' Roy Williams
Gerald Laird: Los Angeles Rams' Eric Dickerson retro
Jerry Hairston: Bears' Walter Payton throwback
"[The players] are fantasy football guys, but I'm just a Sunday football guy," Washington said. "I'm a Saints guy when they win, I'm an aints guy when they lose."
He said it:
"It always runs through my head, because I'm curious what it would have been like to be part of that rotation. But KC gave me an opportunity to play, and I can't deny that fact. [In Oakland], I was ahead of [Joe] Blanton in the rotations throughout the Minors, so I always wonder what would've happened if I stayed." -- Rangers reliever Mike Wood, who was the Athletics' 10th-round Draft pick in 2001
Sammy Sosa was named Latino Player of the Year by Latinobaseball.com. Sosa was honored before Sunday's game against the Athletics. ... Washington is hopeful Blalock can return and play third base by the end of the upcoming 10-game road trip. ... The Rangers would like Jarrod Saltalamacchia to play winter ball, but he has family obligations. Saltalamacchia's wife, Ashley, is going through a difficult pregnancy with their second child. Saltalamacchia will still attend the instructional league for a week to 10 days this fall. ...Class A Clinton, the only Rangers' Minor League affiliate still playing, lost the first game of the three-game playoff series to Beloit, 6-1. Clinton took two of three from Cedar Rapids to advance, but was held to just four hits on Saturday.
Texas begins a nine-day, 10-game road trip starting with a doubleheader at Detroit on Tuesday, with the first game scheduled for 12:05 p.m. CT at Comerica Park. Right-hander Vicente Padilla pitches for the Rangers against right-hander Chad Durbin in Game 1. In the second game, scheduled for 6:05 p.m. CT, McCarthy pitches for Texas against right-hander Jair Jurrjens of Detroit.