As Stephie and Opcode and Jonathan Wood all said, don't give a kitty a treat for this: treats act as rewards for the kitty herself doing something good, such as letting you comb out a knot or clean her eye, or doing something you personally think is a good idea. (In Skinner-Psychology terms it's reinforcement, part of Operant Conditioning.)
It's difficult to apologize to cats: with dogs, submissive behavior works well (although one must, as Opcode noted, be quite careful here). Some cats understand submissive behavior but it's generally not productive. Soothing, friendly behavior on your part is good though: slow blinks, petting, or "voice petting", if your cat responds to these.
Cats will mostly shrug off this kind of accident, though the time duration depends on the cat's personality. Cats that are themselves easily frightened and submissive (shy, retiring, etc) will take longer to recover—but this is kind of tautological, as we define their shyness in terms of how quickly they react to negative feedback.
Most of my cats like to "follow from in front" and I trip over them a lot. They don't mind, though I do on the stairs! I tell them that if they're going to follow from in front, they need to keep going. 😀
I keep my shoes off at home, so it's not so bad for them, but my scared-y cat is scared of shoes (which is wise of her: I can't feel the stepping-on-tail so easily with the shoes on!).