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?