I'm 6'4" and here are the things that make me uncomfortable when riding.
-Short horses for two reason. One is it makes me feel like my feet are going to plow the arena at any moment. Second is your legs typically go below their chest which makes it feel like I have nothing to hold onto with my legs and will end up under their belly. Ask for a bigger horse if using a small one.
-Stirrup length. Since you said knees are up to the saddle I'll assume you are riding english. Us tall people generally don't like our legs set up that tall even if it's the "proper" seat. Lengthen those stirrups and see how it feels. I ride with my knees barely bent and if I stand up in my stirrups my butt clears the saddle by only a bit. You don't have to go as long as I do, I used to ride with them shorter but then my knees starting hurting on longer rides.
-Saddle fit is very important for proper balance. Another guess on my part you don't have your own saddle and using a saddle the trainer provided. They probably put you in the largest saddle they own due to your height, that doesn't mean it's a good fit. Could be to small and even to big if you have a small butt.
-If you are using an english saddle, try a western or aussie if available. They provide more support and as a beginner will likely make you feel like your seat is more secure. Riding in an english saddle does take more leg and core strenght than using the other two types.