bereuen
to regret
To feel regret and remorse about a past action or decision and wish one had acted differently.
Er bereute es zutiefst, seine Freunde angelogen zu haben.
He deeply regretted having lied to his friends.

to regret
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to regret
To feel regret and remorse about a past action or decision and wish one had acted differently.
Er bereute es zutiefst, seine Freunde angelogen zu haben.
He deeply regretted having lied to his friends.

'Bereuen' (to regret) is derived directly from the noun 'die Reue' (remorse/regret). When you regret something, you feel remorse about it.
Er zeigte keine Reue für seine Tat.
He showed no remorse for his act.
The verb 'bereuen' (to regret) can be used in three ways: with an accusative object, with a 'dass' clause, or with an infinitive construction with 'zu'.
Ich bereue meine Worte.
I regret my words.
Common things people regret are 'eine Entscheidung' (a decision), 'eine Tat' (an act/deed), or 'Worte' (words). The feeling is often intensified with adverbs such as 'zutiefst' (deeply), 'bitter' (bitterly), or 'sehr' (very much).
Später hat er seine Entscheidung bitter bereut.
Later, he bitterly regretted his decision.
to apologize / excuse
'entschuldigen' and 'bereuen' can both be important after a mistake or a wrong decision. 'Sich entschuldigen' means to apologize and is an outward action: you speak to the person affected and ask for forgiveness. 'Bereuen' is mainly a feeling: you see your own earlier action as bad and wish you had acted differently. You can regret something without apologizing. And you can apologize even if you only want to be polite. So the words are easy to confuse, but they emphasize different sides.

Beim Frühstück bereut Mila, dass sie den Termin vergessen hat.
At breakfast, Mila regrets forgetting the appointment.
Nach dem Einkauf entschuldigt sich der Kunde für seinen Ton.
After shopping, the customer apologizes for his tone.