The piece failed, causing helium to overpressurise an oxygen tank in the second stage, which led to the explosion, he said.
But Musk also pointed to another possible cause, saying that as the company continues to grow it may have lost some of the inherent paranoia that fueled SpaceX in its early days, when it was unclear whether the Internet tycoon and his loyal band of rocket scientists would ever be able to reliably pull off space launches.
The explosion was the "first time we've had a failure in seven years," Musk said. "To some degree I think the company as a whole maybe became a little complacent."
Musk is a notoriously hard-charging executive, who operates on little sleep, fires off tweets in the middle of the night and famously keeps his desk where everyone can see how many hours he dedicates to his companies, including Tesla Motors.
He is an obsessive who sweats every launch, and he wants his employees to as well, which is why he fires off an email before each flight, telling them that if they blow the whistle on a problem, they will be protected even if they go over their managers' heads.
"They should call me immediately on my cellphone or send me an email," he said.
Watch:
Raw: SpaceX rocket blows up after liftoff
In the call with reporters to discuss the results of the preliminary analysis of the explosion, Musk detailed how a faulty strut designed to withstand 10,000 pounds of force buckled under 2,000.
But he sounded at times as if he were giving a business-school lecture on how a successful start-up can retain its innovative culture and edge as it grows into a corporate behemoth.
SpaceX has had an extraordinary string of successes - winning contracts from NASA to fly cargo and, eventually, astronauts to the space station. It has forced one of its main competitors, the United Launch Alliance, the joint venture between Lockheed Martin and Boeing, to reconfigure its business to compete with SpaceX.
But after becoming a darling of the space industry with one successful flight after another, Musk said he fears that the company's winning streak has perhaps softened it.
When the company lost a string of rockets in its early days, there were only 500 people working at SpaceX, he said. Now the company employs 4,000.
"The vast majority of the people at the company today have only ever seen success," he said. "You don't fear failure quite as much."
(The company did lose an unmanned test rocket, which exploded over Texas last year.)
The 20th email asking people to come forward doesn't "resonate with the same force," as it did when the company was small and scrappy and feared going out of business. "There's Elon being paranoid again," he said of the reaction.
But now employees know the driving power of failure - and fear - "and we'll be the stronger for it," he said.
Musk wouldn't say exactly when the company will fly again, revealing only that it would be "no sooner than September."
The Dragon capsule, which was carrying the space station's supplies, survived the explosion, Musk said, and was communicating with the control centre until shortly before it crashed into the ocean. If it had been outfitted with additional software, the parachutes would have deployed, Musk said, and the capsule could have been saved.
The capsule the company is developing to ferry astronauts to the station is equipped with thrusters that would have flown the astronauts to safety, he said.
The faulty strut is manufactured by a supplier, not SpaceX, Musk said. He declined to name the supplier.
He said that the investigation into the explosion being conducted by SpaceX in conjunction with the Federal Aviation Administration and NASA is ongoing and that it could turn up causes other than a failed strut.
But for now, he said, "there doesn't seem to be any other explanation that makes sense."
