It turns out that the OED does attest a verb (and resulting noun) disesteem. They suggest that it may be related to its French cognate désestimer from the 16th century, or to the equivalent Italian version, disestimare. I get the feeling these were used more way back when than they are now.
The OED gives to disesteem as a transitive verb whose first (and only non-obsolete) sense is:
To regard with the reverse of esteem; to hold in low estimation, regard lightly, think little (or nothing) of, slight, despise.
- 1594 Daniel Cleopatra Ded., ― Ourselves, whose error ever is Strange notes to like, and disesteem our own.
- 1629 Lynde Via tuta 195 ― The authority of Prelates would bee disesteemed.
- 1735 Wesley Wks. (1872) XIV. 208 ― Nor will he at all disesteem the precious pearl, for the meanness of the shell.
- 1868 Helps Realmah (1876) 262 ― Thinking that he had somehow or other offended Ellesmere, or was greatly disesteemed by him.
That’s the verb; also per OED, the noun is:
The action of disesteeming, or position of being disesteemed; want of esteem; low estimation or regard.
- 1603 Florio Montaigne (1634) 66 ― The Turkes, a nation equally instructed to the esteeme of armes, and disesteeme of letters.
- 1670 Milton Hist. Eng. ɪ. Wks. (1851) 1 ― Disesteem and contempt of the public affairs.
- 1697 Dryden Virg. Past. Pref. (1721) I. 76 ― Pastorals are fallen into Disesteem.
- 1754 Edwards Freed. Will ɪᴠ. i. 195 ― Their Worthiness of Esteem or Disesteem, Praise or Dispraise.
- 1810 Bentham Packing (1821) 91 ― Whatever tends to bring a man in power into ‘disesteem’.
- 1884 Pennington Wiclif ii. 32 ― The prevailing disesteem in which the Scriptures were held.
This Google N-gram suggests that while not quite unknown, that it has even less currency than do disparage or deprecate:
Gosh, they were certainly more negative back in the 19th century, weren’t they now? :)
Sure, it’s kind of old-fashioned, but it does seem to exactly match your desired sense. It’s probably better than the (only deceptively, as it turns out) modern-sounding disrespect, and doesn’t carry the overtones of active disapproval that disparage does.