How would you depict that with a pair of eyes and a mouth?

I've always thought U+01F97A FACE WITH PLEADING EYES does an okay job of representing loneliness. If you were to tint U+01F616 CONFOUNDED FACE green, it would be good for jealousy, perhaps.

You are thinking about particular renderings of emojis. The actual definition for U+01F97A FACE WITH PLEADING EYES does not represent loneliness at all and you can't expect that whatever shows up for whoever you're talking to does. But people do keep adding these expectations to emojis that are not encoded in unicode at all so while emojis do give the impression of being a standardized encoding we're really back to vendor-specific codepages.