We cannot submit form (i.e., Google created internally using jQuery) directly. You have to change your code to change look and feel. Here is the one you are looking for:
<form id="cse-search-box" action="http://google.com/cse">
<input type="hidden" name="cx" value="YOUR SEARCH ENGINE ID goes here" />
<input type="hidden" name="ie" value="UTF-8" />
<input type="text" name="q" size="31" />
<input type="submit" name="sa" value="Search" />
</form>
<img src="http://www.google.com/cse/images/google_custom_search_smwide.gif">
Reference: https://support.google.com/customsearch/answer/1351747?hl=en