Go to your WordPress admin area, => Pages
and open (edit) your contact page (the one where you placed the shortcode from Contact Form 7
inside). Now on the top-right side of the page you will see "screen options". Open that and checkmark "Discussions":
Now scroll down and find the options to switch on/off the discussions. That's the place where you uncheck "allow comments"
Save your settings and that's it.
Let me know when you have it sorted.