Tam olarak aradığınız şey bu mu bilmiyorum ama bu şekilde yapılabilir.



<div class="row form-contact" id="IletisimForm">
    <form id="contact-form" class="label-placeholder" action="ajax.php?p=iletisim" method="post">
      <div class="row clearfix">
        <div class="form-group">
          <input id="contact-name" type="text" name="name" class="input-control" placeholder="<?=dil('TX32');?>">
        </div>
        <div class="form-group">
          <input id="contact-email" type="text" name="email" class="input-control" placeholder="<?=dil('TX33');?>">
        </div>
      </div>
      <div class="form-group">
        <textarea id="contact-textarea" class="input-control" placeholder="Mesajınız" name="message"></textarea>
      </div>
      <div class="form-group">
        <div class="g-recaptcha" data-sitekey="keyid"></div>
      </div>
      <div class="form-group">
        <button style="cursor:pointer;font-family:Titillium Web;" type="submit" class="btn btn-alter btn-border btn-border-brown" id="submit-contact"><?=dil('TX34');?></button>
      </div>
    </form>
  </div>
  <div class="row form-contact" id="Gonderildi" style="display:none">
    <?=dil('TX91');?>
  </div>
  <script src="https://www.google.com/recaptcha/api.js"></script>