I feel frustrated when people use the word “feel” incorrectly.
I feel they don’t know how to write well.

The first sentence uses the word “feel” correctly. The second does not.

Simple rule of thumb: If what you’re “feeling” is more than a single adjective’s worth, it’s not a feeling. Use “think,” “believe,” “surmise,” “expect” or some other verb that describes brain activity, not emotion. Check out http://www.thesaurus.com/browse/think for some ideas.

If it just, well, feels right to use “feel” instead, plug in that single adjective after it:

We feel the conference will be a success.
We expect the conference will be a success.
We feel confident the conference will be a success.