Miller, an eight-time Pro Bowl selection, told ESPN's NFL Live on Friday that he had tried to take every precaution over the past month, but he still contracted the virus.
"What keeps me at peace is knowing I did everything I was supposed to do," said Miller, who announced Thursday he had tested positive and is now resting at home. "I was here at home. I've been here at home for about a month now, and I've probably left the house a total of four times. And when I left, I didn't get out of the car or anything like that.
"I didn't have any contact. I was just riding with my brother up the street to get some food. I literally took it serious, I wasn't out and about. It hit me right here in my house."
Miller, who has asthma, said Friday he elected to get tested after he had started to have a cough about six days ago and his inhaler "wasn't working like it normally should."
"It's very, very serious," Miller added. "It's my job to keep my body in tiptop shape, and I feel my body is in tiptop shape. If I can get this, anybody can get this."
Miller said he had limited contact with teammates over the past few weeks. He said Broncos kicker Brandon McManus, who is his closest friend on the team, had visited "about 15 days ago" and that just a few people had been to his house, including a plumber and somebody who serviced his fish tanks.
"It's not like a movie where you can say, 'OK, got it from this guy,'" Miller said. "It's just too many different factors. ... We tried to keep the bodies low and keep everything down."
Miller had spent time training in the San Francisco area immediately following the season, but he returned to Colorado shortly before the stay-at-home order in the Bay Area went into effect March 16.
Miller isn't sure when the NFL should consider letting teams get back to work in their facilities, let alone resume playing games.
"Whatever is safe. ... My vote is to do whatever is safe," Miller said. "This is a very, very serious disease. And I have all the resources here for me, I have a team physician right down the street. I'm fortunate to have somebody that can go get groceries. I was fortunate to have attention. There's so many other people out there, that's not the case for them. This is a very, very serious disease, and I feel like everybody should take it serious.
"... We've got a lot of intelligent minds on this thing. I feel like we should all just do whatever is safe, take the safest step possible. People want sports and people want to be safe. There's got to be some merger. It's 2020, there's got to be something we can work out."