laugh off vs disregard

laugh off is not a noun while disregard is a noun.

Word	Noun	Adjective	Verb	Adverb
laugh off	No	No	Yes	No
disregard	Yes	No	Yes	No

As verbs, disregard is a hypernym of laugh off; that is, disregard is a word with a broader meaning than laugh off:

Other hypernyms of laugh off include brush aside, brush off, discount, dismiss, ignore, push aside.

laugh off (noun)	disregard (noun)
	willful lack of care and attention
	lack of attention and due care

laugh off (verb)	disregard (verb)
deal with a problem by laughing or pretending to be amused by it	give little or no attention to
	bar from attention or consideration
	refuse to acknowledge