Michael O'Neill's side qualified for the last-16 stage of the competition after finishing as one of the four best third-placed sides in France.
On Saturday, Northern Ireland will take on Wales in the first knockout round and Lafferty sees no reason why his nation cannot "upset a few teams" at the championships.
"Wales will be a tough game. They have world-class players. With our heart and determination, we believe we can beat anyone. I think we can go the whole way. It might take some luck - but every team needs luck. We'll upset a few teams," Lafferty told reporters.
Northern Ireland will enter the Wales match off the back of 1-0 defeat to Germany in their final Group C clash on Tuesday night.