Someone who feels insignificant or unimportant feels that they aren't special. Such a feeling is typically accompanied by the desire to be considered special by someone. These words can therefore be used to imply the feeling you seek in general. For example, "I wish I wasn't so insignificant." can be safely taken to mean "I wish someone would think I'm significant/special."
Another related possibility is the concept of validation. A person seeking validation is looking for another person to validate their existence, i.e. to confirm that their existence isn't meaningless, pointless, or inconsequential in the validation provider's opinion. Often, someone seeking validation is even looking to be praised or appreciated.