Mild:
* Dislike: A general lack of enjoyment or approval.
* Deprecate: To express disapproval of something.
* Disapprove: To have a negative opinion of something.
* Take exception to: To find something offensive or unacceptable.
* Find fault with: To criticize or point out flaws in something.
* Be unimpressed with: To not be impressed or moved by something.
* Not care for: To have no particular interest in something.
* Have no use for: To not find something valuable or useful.
Moderate:
* Condemn: To strongly disapprove of something, often publicly.
* Repudiate: To reject something completely.
* Abhor: To hate something intensely.
* Despise: To have a strong feeling of contempt for something.
* Scorn: To treat something with disdain or contempt.
* Detest: To have a strong feeling of aversion to something.
Strong:
* Loathe: To feel extreme hatred or disgust towards something.
* Abominate: To find something utterly repulsive or detestable.
* Execrate: To curse or denounce something vehemently.
* Revile: To use abusive language towards something.
* Vile: To consider something morally repugnant or despicable.
Other words that convey a lack of appreciation:
* Resent: To feel bitterness or indignation about something.
* Be offended by: To be upset or insulted by something.
* Take offense at: To feel insulted or offended by something.
* Feel wronged by: To believe you have been treated unfairly.
The specific word you choose will depend on the context and the strength of your feelings.