Does cancelling a credit card hurt your credit?

I have a few credit cards that I’ve torn up and don’t use, but I didn’t cancel (I’ve never had any debt I always paid them off every month). But I have one credit card that has a yearly fee of $60. I have no need for it so I figured I might as well cancel it and save the $60. I was just curious if closing a credit card negatively affects your credit score? I know it will subtract from my “total credit” available, but is that really a big deal?

Thanks