In his first public acknowledgment, Washington apologized Wednesday for his behavior, eight months after he told Rangers president Nolan Ryan, who turned down the manager's offer to resign.
"I made a huge mistake and it almost caused me to lose everything I have worked for all of my life," Washington said at a news conference Wednesday. "I am not here to make excuses. There are none."
Washington said he used cocaine only once and called it "stupid" and "shameful."
The failed test first was reported by SI.com.
Washington said he told the commissioner's office and Rangers officials about using cocaine before he had a routine drug test.
"He came forward and said he would resign," Ryan said. "He understood the consequences. We had a lot of discussions and a lot of soul-searching on it."
"He stood up to it. We felt like he was sincere and forthright," he said. "We are very disappointed by this. We are upset we were put in this position."
Washington met with his players earlier in the day and told them about testing positive in July.
"He was very emotional, you could tell that he's a broken man from this one bad choice he made," Texas star Josh Hamilton said.
Hamilton has a long history of drug abuse and was suspended for the 2004 season when he was in the minors for Tampa Bay. The All-Star outfielder is the most prominent player in the last decade to be disciplined for a so-called recreational drug.
Hamilton has been outspoken about his crack cocaine habit. He said there were no parallels between his problems and Washington's admission of one-time use.
"I was addicted to drugs. All I cared about was getting more and using more drugs. I didn't care who I hurt," Hamilton said. "This was something of a weak moment, a decision of choice ... Our stories are nothing alike. The fact is he made a mistake. He learned from it very quickly. I made a mistake a few too many times and didn't learn from it."
Hamilton said he could understand how a 57-year-old man could use the drug only once.
"You either like it or you don't like it. Either you do it once or you do it more than once," Hamilton said. "That's the way it is. I know people from my past that have done it once with me and have not liked, have not cared for it."
Six-time All-Star Michael Young said his Texas teammates were behind their manager.
"Based on the kind of person that Wash is, the kind of person that we know him to be, we support him 100 percent," Young said. "This isn't going to be any kind of distraction in terms of us getting ready for the season. I think if anything it's going to make us rally around him even more."
"Wash is a good man, first of all," Young said, "and I know what kind of guys are in the clubhouse. We have a bunch of guys that play hard and the right way. I think they took on Wash's personality in terms of that. Like I said, he made a mistake, came clean and I think it's a dead issue."
Washington has been subject to increased testing since he failed, and said he has passed every subsequent test. He said he has completed the MLB drug treatment program.
Management has a different set of drug-testing rules than the ones for players on 40-man rosters that were negotiated by Major League Baseball and the players' association.
For management employees who test positive for cocaine and other recreational drugs — as opposed to steroids and performance-enhancing drugs — treatment is mandatory and decisions on discipline are made by the team and MLB on a case by case basis.
Cocaine was baseball's biggest drug problem in the 1980s, when Dave Parker, Keith Hernandez and several other stars were penalized. Steroids and performance-enhancers have been a far bigger focus in the past decade.
Washington's contract was extended last year for 2010 before the drug test. His contract expires after this year, which will be his fourth with Texas. The Rangers, out of the playoffs since 1999, stayed in postseason contention until late in the year and finished 87-75.
"Here's the biggest question: How and why did this happen?" Washington said. "That's a question I have had to face in numerous sessions with counselors."
"I recognize that this episode was an attempt to dodge personal anxieties and personal issues I needed to confront," he said. "That was the wrong way to do it. It was self-serving, and believe me, not worth it. I know you will ask, and so here's the answer: This was the one and only time I used this drug."
Asked whether he believed Washington's explanation, Ryan said: "I don't know the circumstances, but after Major League Baseball investigated it, they came back and felt like it was a one-time incident. Ron expressed that to us."
Rangers general manager Jon Daniels said team management was initially "shocked, disappointed, angry" when Washington told them about his drug use.
"We felt it was important he acknowledged doing what he did. That was our first priority," Daniels said.
Hamilton, who said he knew nothing of Washington's cocaine use until Wednesday, said the matter was rightly handled privately by the organization.
"Really everything was taken care of like it needed to be," Hamilton said. "Somebody just felt like they needed to run their mouth and caused a stir. At the same time, the stir didn't affect us. You know we're a team. We're pulling behind Wash. We respect him more than anybody. For me personally as a player, I feel real privileged and honored to have Wash as a manager because he is a guy you can trust, a guy you can look to and know he's going to do the right thing."
Hamilton said he thought he knew the source of the initial story.
"Not somebody with the organization anymore," he said, "and it's a good thing they're not."
He didn't elaborate.
Washington has been a supporting figure for Hamilton, who acknowledged his sobriety had lapsed when he drank in a Tempe bar in January of 2009. Hamilton's public confession came last August after a Web site published photos of him cavorting with several scantily clad women.
"Walking in today, hearing what Wash had to say, it really doesn't change how he supports me, how he supports my recovery," Hamilton said. "Like I said before, I look at Wash, Wash is not an addict, he's not addicted to drugs. He didn't ruin his life. It didn't take him in directions he didn't want to go. He made that one mistake, he manned up to it. He's somebody I'm going to draw inspiration from, especially after this."
Washington had been a coach with the Oakland Athletics for 11 years when Texas hired him in November 2006. His only prior managerial experience had been two years in the low minors.
Washington played 10 seasons in the majors, mostly as an infielder for Minnesota in the 1980s.