Williams was one of four people interviewed by the Rockies, and after what was said to be a strong interview, he narrowly lost out to Walt Weiss.
"Matty was Matty," Rockies general manager Dan O'Dowd said. "He was prepared, organized with his thoughts, paid attention to detail and he was passionate. He came across so clear in what he wanted to do. There's no doubt in my mind he's going to be a big league manager real soon."
While disappointed that he did not get the job, Williams appreciated the experience of going through the interview process for the first time. He spent nearly 10 hours talking baseball with Rockies senior vice president of baseball operations Bill Geivett and also met with O'Dowd and Rockies owner Dick Monfort at Coors Field.
"I enjoyed the process, I enjoyed the opportunity to go experience that," Williams said. "I enjoyed my time with Bill Geivett, Dan O'Dowd and Dick Monfort. Ultimately they decided to go in a different direction, but the experience is something that I appreciate. You never know until you get in one of those situations what it's going to be like."
Williams said he received support from D-backs GM Kevin Towers, manager Kirk Gibson, his fellow coaches, team president Derrick Hall and managing general partner Ken Kendrick during the process.
"Their policy as an organization is they want people to succeed and they've all been great about me getting an interview and possibly taking the next step," Williams said. "That was great because it means a lot to have the support of people you respect and admire."
Williams was known for his power at the plate and intensity on the field during a 17-year Major League career with the Giants, Indians and D-backs from 1987-2003.
In his three seasons on the Arizona coaching staff, Williams has become respected for his work with the team's infielders and his cerebral approach to the game.
"I heard from both Dan and Givo that Matty did a great job and I'm not surprised," Towers said. "I didn't know him that well when I came to the Diamondbacks, played against him when I was younger, knew of him, watched him play, admired the way he played. But when I was around him and listening to him speak, he's very articulate and I was very impressed."
Gibson has heartily endorsed Williams and was effusive in his praise for him when Williams was named manager of the Salt River Rafters in the Arizona Fall League this year.
The Rafters won their division and will play in the AFL's Championship Game on Saturday.
The Blue Jays asked the D-backs for permission to talk to Williams about their managerial opening, but while he spoke briefly with Toronto GM Alex Anthopoulos last month, he has yet to receive a formal interview.
"There's no question we'll get other people who ask about him if not this year than in the future," Towers said. "He's solid, he's ready, he's prepared."
While Weiss takes on the challenge of managing a team for the first time, Williams will return to the Arizona coaching staff.
"Now I'm focused on being the best third-base coach I can be," he said. "I'm excited about the season because I think we've added some great pieces and I think we have a chance to get back to what we were a couple of years ago."