Tetatnus shots are good for 10 years, so, unless you have had a very nasty cut from a dirty object or burn, you should be fine. Continue to keep the area clean and us a triple antibiotic cream on it as well such as Neosoporin.
If you got a tetanus shot 3 years ago, you're protected, whether or not you missed the dose as a kid.
You're fine, but there are other infections you might get, so just keep the area clean and watch for redness and inflammation. It shouldn't be serious - just treat it like any other cut or scrape.