The fuel efficiency of an automatic car depends on factors like the type of automatic gearbox it has, as well as the engine size and fuel type. There are also several other things that can influence the fuel efficiency of any vehicle, including your driving habits and how laden your car is.
Automatic cars previously tended to use more fuel than manuals, but modern automatic transmissions offer more efficient gear selection and changes. That means they can match or even outcompete some manual cars in fuel economy.