Words that mean ''to say something unintentional''

To blurt or blurt out.

from Wiktionary:

blurt [Verb]:

To utter suddenly and unadvisedly; to speak quickly or without thought; to divulge inconsiderately — commonly with out.

• Please think about your reply and don't just blurt out the first thing that comes to mind.

Further to comments to the OP:

• to "put your foot in your mouth" is to say something embarrassing, and
• to "spill the beans" is to tell the facts about something (presumably intentionally).
• To let something slip is to unintentionally reveal a fact which you should have kept secret — is this the meaning you wanted?