The term parallel to 'doggerel' in the sense you intend, but "general to art", would be an adjective rather than a noun, modifying the noun applied to the particular art form ('music', 'painting', 'sculpture', etc.).
Not æsthetic; void of æsthetic perception or taste.
["inaesthetic, adj.". OED Online. June 2016. Oxford University Press. http://www.oed.com/view/Entry/93049?redirectedFrom=inaesthetic (accessed July 08, 2016).]
Alternatively, and perhaps more precisely but less frequently used,
unaesthetic (ˌʌniːsˈθɛtɪk) adj
1. not beautiful
2. not in good taste
(Collins English Dictionary – Complete and Unabridged, 12th Edition 2014. S.v. "unaesthetic." Retrieved July 8 2016 from http://www.thefreedictionary.com/unaesthetic )
The true aim of all art is esthetic quality (beauty), and insofar as art is effective or good it achieves that aim. "Bad" or "ineffective" art may aim for other goals--inculcation of morality, entertainment, promotion of right knowledge, etc.--or may simply miss the esthetic goal entirely due to the ineptitude of the artist.
This answer, however, sets aside a common understanding of 'doggerel' in favor of the sense you intend. 'Doggerel' is not universally understood to be "ineffective". Quite the contrary, 'doggerel' is often defined as effective in achieving particular goals (inaesthetic in themselves, but perhaps subordinated to an overall esthetic goal proper to art) by reason of its crudity:
loosely styled and irregular in measure especially for burlesque or comic effect; also : marked by triviality or inferiority.
(Merriam-Webster, emphasis mine)
Doggerel, a low, or trivial, form of verse, loosely constructed and often irregular, but effective because of its simple mnemonic rhyme and loping metre. It appears in most literatures and societies as a useful form for comedy and satire. It is characteristic of children’s game rhymes from ancient times to the present and of most nursery rhymes.
(Encyclopædia Britannica, emphasis mine)