Saying you don't want something you do because you were denied it

Sour grapes, after one of Aesop's fables; here's the version from the old Harvard Classics:

ONE hot summer’s day a Fox was strolling through an orchard till he came to a bunch of Grapes just ripening on a vine which had been trained over a lofty branch. “Just the things to quench my thirst,” quoth he. Drawing back a few paces, he took a run and a jump, and just missed the bunch. Turning round again with a One, Two, Three, he jumped up, but with no greater success. Again and again he tried after the tempting morsel, but at last had to give it up, and walked away with his nose in the air, saying: “I am sure they are sour.”

[moral]:     “IT IS EASY TO DESPISE WHAT YOU CANNOT GET.”

In psychology, it's called rationalization.

The most commonly used defense mechanism, in which an individual justifies ideas, actions, or feelings with seemingly acceptable reasons or explanations. It is often used to preserve self-respect, reduce guilt feelings, or obtain social approval or acceptance. - - Medical Dictionary.

Examples of rationalization (from Wikipedia)

• "I didn't get the job that I applied for, but I really didn't want it in the first place."

Some rationalizations take the form of a comparison. Commonly this is done to lessen the perception of an action's negative effects, to justify an action, or to excuse culpability:

• "At least [what occurred] is not as bad as [a worse outcome]."
• In response to an accusation: "At least I didn't [worse action than accused action]."
• As a form of false choice: "Doing [undesirable action] is a lot better than [a worse action]."

Saving Face Going along with something to protect your dignity, not lose respect with peers and to not be excluded societally.

Yes, in psychology there is a description for this behaviour. It's called:

"eliminating a cognitive dissonance".

This is actual a self-preserving mechanism or a coping strategy. It allows us to handle situations that we have little or no control over.