I'll say it again, but in a different way, you've only done the first half.
Read the link I posted above, it's literally step two of implementing it yourself and starts:
"This page explains how to verify a user's response to a reCAPTCHA challenge from your application's backend. When a reCAPTCHA is solved by end user, we will return a user response token.
..."
It doesn't even try to prevent the form being sent!
If you were a bot writer, would you bother implementing a full JavaScript stack if it worked fine without JavaScript?