Learn Italian: Non abbiamo nessun'esigenza di inventare un pretesto.

Esigenza is a feminine noun starting with a vowel. The feminine adjective nessuna drops its final -a and replaces it with an apostrophe before a vowel to make pronunciation flow better. Note that if the noun were masculine and started with a vowel, you would just use nessun without an apostrophe.

Why do we use Non at the start of the sentence if nessun' already makes it negative?

Italian requires a double negative when the negative word comes after the verb. Because nessun'esigenza comes after the verb abbiamo, you must put non before the verb. Literally, this translates as: We do not have no need.

Why is the preposition di used before inventare?

The noun esigenza requires the preposition di to connect it to a following infinitive verb. You might remember this exact same pattern from avere bisogno di (to have need of or to need to). So, avere esigenza di simply means to have a need to do something.

Could I use bisogno instead of esigenza here?