The Astros hired Nationals third-base coach Bo Porter, but Martinez saluted the Astros for the class they showed during the process.
Martinez received a call from Astros general manager Jeff Luhnow after the Rays boarded the bus following Wednesday night's win over the Red Sox at Fenway Park.
"Houston has a great oganization," Martinez said. "Some fantastic people and I wish them the best."
Not getting the job did not change Martinez's resolve to one day manage in the Major Leagues.
"Eventually, I want to manage," Martinez said. "If it were sooner, great, but just because I didn't get the Houston job doesn't mean that I don't feel like I can't manage.
"I know one day I'm going to manage. When the opportunity rises, it's going to be the right fit. And everybody's going to be happy."
When asked about other possible openings, Martinez said that his focus remains on what's happening with the Rays.
"Getting back to the playoffs and enjoying the moment right now that we're in," Martinez said. "Right now, if you can't be excited about what we're doing here, this has been great. I tell the guys, 'When you're playing for something in September, it's awesome, you know."