It’s in the OED:
Expressing frustration at the realization that things have turned out badly or not as planned, or that one has just said or done something foolish. Also (usu. mildly derogatory): implying that another person has said or done something foolish.
The best part is when it was first used: not by Homer Simpson, but in a 1945 BBC radio show.
Hat tip to Eric Lawrence.
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I always thought it was D’oh!
Supposedly, doh / d’oh never appears in a Simpson’s script and instead appears as “annoyed grunt.” There’s an episode called “E-I-E-I-(Annoyed Grunt).”
Technically “doh” is a short for “damn” and “oh.” Also, the second point seems to define “duh,” pronounced and used differently than the annoyed grunt.