How can I save face after asking a guy out and getting rejected?

I told a guy that I work with that I thought he was lovely and if he'd like to hang out sometime. At first he said yes. then he said he was sort of hanging out with someone and that it was complicated. I actually turned beet red and said I was sorry that I made things awkward and that I felt embarrassed. He said "don't feel bad. I'm flattered. that take guts. I would have hung out with you but you seemed to react negatively when I said I was sort of hanging out with someone." The problem is I have to see this person for work. I'd like to not be a constant ego-boost for them every time he sees me.

How can I save face after asking a guy out and getting rejected?
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