The seven-time Tour De France winner and the Grammy-winning rocker announced their breakup in a joint statement last week after "much thought and consideration," despite their "deep love and respect."
Armstrong acknowledged the split in his Sunday night talk show, "Armstrong Radio," on the Sirius Satellite Radio channel "Faction," saying he was "torn it didn't work out."
"Obviously, this week was a rough week for us, but that doesn't change the fact that Sheryl is an unbelievable lady, one of the smartest, wisest, most gifted people I've ever met and a person that I can honestly say has shown me a love that I never knew," he said.
"It's only fair that I say that, and it's only fair that we play one of her songs tonight and not run from the situation."
Crow, 43, has called Armstrong, 34, the inspiration for her last album, "Wildflower," which was released in September.
They announced their engagement in September. It would have been her first marriage and his second. He has three children from a previous marriage.
Following the breakup announcement, Armstrong reportedly canceled his scheduled appearance as a presenter at the 48th annual Grammy Awards on Wednesday. A call to the Recording Academy by The Associated Press was not immediately returned Tuesday.
Crow is up for three Grammys: best pop vocal album ("Wildflower"), best female pop vocal performance for "Good Is Good" and best country collaboration with vocals for "Building Bridges."