A straight right to the heart is the "natural" counter to a left jab. It works wonders to "shorten" an opponent's left arm, really discouraging him from using that punch. Very simple to execute, as well, because in essence all you are doing is throwing a straight right hand: when you put your weight on the left foot (slide it forward and left a bit if you choose-how much depends on what you intend to do next) and turn your hips and shoulders it should lower your body enough to let the jab go by.
A parry is nothing at all like the Karate Kid. Based on timing- entirely on timing-it is always a minimal movement, often a flick of the wrist. Never reach out to parry- let the punch come to you. Buddy McGirt used to parry a lot and Julio Caesar Chavez used to parry a ton of right hands with his left glove. James Toney, at 168 and 175 especially, used to parry jabs over his left shoulder then bring his jab up and under while pushing forward off his right foot. He scored a knockdown in the 2nd Hembrick fight in this manner.