big, bitter, deep, genuine, great, profound, real, sincere
Her biggest regret was that she had never had children.
She expressed deep regret at the incident.

pang, stab, tinge (esp. BrE), twinge (esp. AmE)

feel, have
I have absolutely no regrets about resigning.

express, show
send
He sends his regrets about missing our 45th reunion.

to your regret
To my regret, I lost touch with her years ago.

with regret
It is with deep regret that we announce the death of Mr Fred Fisher.

without regret
She thought of them without regret.

regret about, regret over
She showed no regret about leaving her country.

regret at
my sincere regret at what has happened

regret for
She enjoyed living alone, but felt a tiny pang of regret for her mother's cooking.

expression of regret
The police offered no expression of regret at his wrongful arrest.

a matter for regret (BrE), a matter of regret (esp. BrE)
I never learned to play an instrument and that's a matter of some regret. (BrE)

bitterly, deeply, greatly, really, seriously, sincerely, truly, very much
The president said that his country deeply regretted the incident.

rather
immediately, instantly
I immediately regretted not asking for his name and address.

quickly, soon
It was a decision she would soon regret.

later
Pierre told them some things he later regretted telling.

never

begin to
come to, grow to, live to
She knew that she would live to regret this decision.

seem to

Regret is used with these nouns as the object:
choice, decision, error, fact, incident, inconvenience, indiscretion, loss, mistake, word