how to remove a page that was made private from google search results?

I have a thank you page that I made private, it only appears when clicking on a submit button, but I don't know why it appears first on search results when I google site:mywebsite, I made it private but still appears but as a 404 error page. How can I delete it permanantly from search results?

PS: without using the robots.txt.

Solution

I solved it but submitting a request to take it off in google search console, and it worked.