Correct spelling, explanation: as a rule, whenever there is a y at the end of a word, the y is changed to i when adding a suffix. Most verbs follow this rule with a few exceptions, when there is another vowel before the y in the root word (e.g. play + ed → played, not plaied). In the case of the past tense of cry, the letter preceding the y is a consonant, so based on the principle, the y changes to i, which is why cried is the only correct past tense of cry.

Definition of cried:
Verb, past tense of cry:
1. to have tears coming out of the eyes, usually due to intense emotions or pain
While she was heartbroken, she cried a lot and would not talk to me at all.
2. To call for someone, to shout
‘Stop!’ he cried out, trembling in fear.
3. A noise made by an animal
My new puppy cried all night and scratched the door wanting to go out.

Incorrect spelling, explanation: cried is a regular verb created based on the principles of adding an -ed suffix and exchange of y to i. Regardless of the seemingly logical grammatical structure of cryed, this form is incorrect and inconsistent with the principles of English grammar. Cry ends in a y, which has to be changed into i when adding a past tense suffix -ed. The y at the end of the word remains unchanged only when the preceding letter is a vowel, which is not the case in cry.