For given input file `input` containing the following:

 domain
 demesne

To filter for lines containing `domain`:

 $ awk '/domain/ { print }' input
 domain

To filter for lines _not_ containing `domain`:

 $ awk '!/domain/ {print }' input
 demesne

For filtering based on the _field_ rather than the entire line, we can try the following for the new given `input` file:

 example www.example.com
 exemplar www.example.net

To filter out lines where the first field *contains* `example`:

 $ awk '$1 !~ /example/ { print }' input
 exemplar www.example.net

In your question, you used `$0` which is the entire line rather than the first field.