Google Ngrams shows a marked preference for oop over oops up until 1990:
Is Ngrams to be trusted here? Is it strange that I've never seen oop in writing? Even Dictionary.com doesn't have anything more than acronyms under oop.
Click under the graph to get the actual hits. You find
But I feex you oop goot.
And oop there yonder in those trees,
dominant faces being ∞p (crystallography; this oo is really infinity),
Soo-oop of the ee-evening. Beautiful, beautiful Soup!
as well as a number of other "oop"s, including the call of the sooty grouse. But I didn't see any instances of "oop! I made a mistake." Most of the "oop"s seem to be "up"s spoken with a pronounced accent.
EtymologyOnline says oops is only attested from 1933.
To me it is likely to be a shortening of oops-a-daisy. The Phrase Finder tracks that back to upsa daesy in "The dialect of Leeds and its neighbourhood" in 1862, to up a-dazy from Jonathan Swift in 1711 and to upaday even earlier.
If oop is a dialect form of up, and oops of ups, then you might not be surprised if oop was more common than oops, at least until oops became part of a set exclamation.