catch error message via PHP

I am creating a e-mail form with re-captcha. The form has fields as name, e-mail.

I want to display error message to user only if captcha is wrong, currently form gets refreshed if entered wrong captcha so

<div class="recaptcha_only_if_incorrect_sol" style="color:red">Incorrect please try again</div>

is not working.

Is there any way that I can set any variable as true/false if previous submission was incorrect and later I can display a text in my page later based on that variable?

Thanks