We were disturbed by the way the company tried to cover up the truth. = We were very (very) worried. We were disquieted by the way the company tried to cover up the truth. = We were (quite) worried.

‘Disquiet’ means to make someone uneasy. Example: “I was disquieted by the thunder outside.” ‘Disturb’ has a stronger meaning. Example: “Seeing him yell at his child was disturbing to me.” ‘Disturb’ can also mean to break someone’s concentration. Example: “Please don’t disturb me while I’m studying.”

DISTURB implies interference with one's mental processes caused by worry, perplexity, or interruption. // the discrepancy in accounts disturbed me // DISQUIET suggests loss of sense of security or peace of mind. // the disquieting news of factories closing //