To form the past of should simply add have + past participle:

–I missed my plane this morning. I should have left earlier.

–I can't find a hotel room. I should have made a reservation.

The past form of should conveys the notion of a failure or omission. Note that the customary pronunciation of should have is should've or shouda. The negative form is should not have, pronounced in colloquial English as shouldn't've or shouldn't'a.

Examples of Past of Should

• I was late to work this morning. I should have left the house earlier.
• He misses his girlfriend. He should have gone on vacation with her.