We use should have + past participle to talk about things we regret.
I got really wet walking home last night, I should have taken an umbrella.
The speaker did not take an umbrella when she went out last night so she got wet. She regrets that she did not take her umbrella.
Regret (verb/noun) is to feel sorry about something that happened or did not happen in the past.
I should have called you sooner.
You should have spoken to me before deciding.