I just started with itch.io and I have finished developing a game. But this game contains images that are NOT free for use. So I'm wondering if I'm allowed to publish a project like that on itch.io. Thanks for answers.

Thanks @sman!. Shame that I can't publish it.

Just a clarification: to the best of my knowledge (not speaking in an official capacity) itch.io doesn't police copyrights. If anyone complains, it's on your head. Otherwise, what sman! said. To stay out of trouble, you really do need permission from the creators of all resources you use in your game, whether explicitly granted to you, or implicit in a blanket license, e.g. the open source kind.

Why no try  replacing it with your own art? Doesn't have to be perfect. Mabe better than not releasing at all.

Or if you are lucky you'll find sth that fits at opengameart with a CC0 licence.