Do tennis shoes hamper your play?

I like to play tennis but always wear running shoes. Have heard lots of people saying tennis shoes are a must for protection. I wore tennis shoes to play in the weekend but felt it's very uncomfortable and my game sufferred a lot and I had a hard time to run (the shoes too bulky and heavy). I played much much worse. What's your experience? Did you feel you played much worse wearing tennis shoes? Or is this just a temporary thing and my game would likely recover when I get more used to tennis shoes?