Does "rueful" add a connotation of wry humor versus "rue?"

All other online dictionaries do not mention the wry humorous aspect of rueful . Only vocabulary.com notes that:

The adjective rueful sincerely expresses regret, but it manages to do it with a hint of humor. Rueful shows up a lot in descriptions of remorseful grins or apologetic smiles. If you're sorry about something you've done but you can still laugh at yourself a little bit, you feel rueful. The word itself comes from the verb to rue, which means "to regret."