My dog does the exact same thing when he accidently catches me with his jaw. It's almost always 100% my fault but as soon as he gets a piece of me he immediately drops the toy and starts licking my hand as if to apologize.Yeah, ours does the same thing. Sometimes we have to figure out what she did - most of the time it was just going into a room she isn't allowed in and she went in when we weren't home - but this was different.
She never does anything that gets her into trouble, so this was an actual "I'm sorry". We've played since and it was all normal.
He also has very expressive eyebrows so he emotes quite a bit. Very easy to tell if he threw up somewhere when we get home.
Dogs know when they've done something wrong. They definitely feel remorse.