Why is my cheesesteak meat tough? I made Philly Cheesesteak sandwiches and the resulting meat was quite tough and hard to bite off and chew.

For the meat I used eye of round steak, cut into roughly 3in by 1/8th-1/4th in strips. I did not marinade the meat or season until salt and pepper during cooking. 

To cook the meat I used a nonstick pan over medium heat for a few minutes. 

Is my cut of beef to blame, my technique, or perhaps both?
My experience has shown that you need to slice the meat against the grain when preparing it for sautéing. The shortened muscle fibers make for a more tender piece of meat. After that, the quicker you can cook the meat, the better. Round steak tends to be best either quickly cooked or cooked for an extended period of time -- there's not too much of a middle ground for it.