deep regret; great disappointment
A formal, emphatic expression of regret or disappointment, often used in apologies, condolences, or when conveying unfortunate news.
I feel deep regret about this outcome.
I am very sorry that I could not meet your expectations.
残念 alone means 'regrettable' or 'unfortunate' and is more casual; 大変残念 adds emphasis and formality.
Compound of 大変 (たいへん, 'very') and 残念 (ざんねん, 'regret'). The exact historical derivation is straightforward.