The 23-year-old Scot, who won gold for Britain in the omnium on Friday, returned to the track after a fitful night's sleep to contest the 3km event.
Only the top four riders progressed to a second ride and Archibald finished 0.258 seconds off fourth place.
"I just feel a bit stupid. I wanted to peak for it and I didn't," she said.
"I guess I am just kind of embarrassed as I have put a lot of work into it."
Olympic team pursuit gold medallist Archibald, who clocked three minutes 31.331 seconds, knows there are few opportunities to prioritise a non-Olympic event like the individual pursuit.
The 2018 Commonwealth Games may be her next and final chance ahead of Toyko 2020.
Friday brought Archibald her second world title and first as an individual after her 2014 team pursuit win.
"Yesterday was probably the hardest race I have ever done and it turns out I couldn't do it twice," added the Milngavie rider, who has temporarily relocated to Glasgow from Manchester.
"I had this one chance to focus on it, not that I would have changed yesterday for anything. Definitely no regrets, it was the right thing to do."
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Katie Archibald missed the chance to win another Track Cycling World Championships medal after qualifying fifth in the individual pursuit.