1
general::
Compliment so feebly that it amounts to no compliment at all, or even implies condemnation. For example, The reviewer damned the singer with faint praise, admiring her dress but not mentioning her voice. This idea was already expressed in Roman times by Favorinus (c. A.D. 110) but the actual expression comes from Alexander Pope's Epistle to Doctor Arbuthnot (1733): "Damn with faint praise, assent with civil leer, and, without sneering, teach the rest to sneer."
American Heritage Idioms
2
general::
Phrase(s): damn someone or something with faint praise
Fig. to criticize someone or something indirectly by not praising enthusiastically. • The critic did not say that he disliked the play, but he damned it with faint praise. • Mrs. Brown is very proud of her son’s achievements, but damns her daughter’s with faint praise.
McGrawhill's American Idioms And Phrasal Verbs