I don't think any pep talk anyone can give you will be the rallying cry you're hoping it will be. There's not a soul who can tell you something that will give you the heart and hope to continue. I, or anyone else, can give you our words of wisdom that will help, but 80%+ of finding your motivation is on you and you alone. You're going to want this, or you don't, y'know?
My words of wisdom is the following: Take solace in the knowledge that it is at white belt that the precedents are set. The way in which you study martial arts henceforth is decided at this level. If you're working hard now, you'll work hard later, and you will always ultimately see the benefits of that hard work. While your classmates to whom this "comes naturally" or who "muscle through", they don't understand the need to truly improve their skills now, and so they will not understand that need later on. They slack now, they'll slack later. They will never have good Karate.
I think of it not unlike playing an instrument. There's plenty of those people who play an instrument well, who can impress with their music. But then there's always that one guy in your group of musically inclined friends who never really plays infront of people, doesn't talk much about his music, nothing. Because he doesn't really need to, cause everybody knows that guy can shred better than anybody.
A year, two years, or three from now, those other guys who are in your class now will be walking around with some mediocre skills, but people will know that they practice(d) martial arts, and will think of those guys as tough as nails. Probably nobody will know what you can do, except for those guys who attend(ed) class with you. And those guys who everyone thinks are tough as nails, well, those guys will be secretly thinking that about you, with a voice in the back of their head saying, "I won't mess with him, that boy will put me down. He's just on a different plane."
Be humble. Do your thing. Do it well. Give it time. It'll come.