You can add an ID to the input field – and listen for the input event. Then you have to get the value of the input to use in the selector to get the selected option
$(function() {
$('#browserinput').on('input',function() {
var opt = $('option[value="'+$(this).val()+'"]');
alert(opt.length ? opt.attr('id') : 'NO OPTION');
});
});
<script src="https://ajax.googleapis.com/ajax/libs/jquery/1.11.1/jquery.min.js"></script>
<input id='browserinput' list="browsers">
<datalist id="browsers">
<option id="op1" value="Internet Explorer" />
<option id="op2" value="Firefox" />
<option id="op3" value="Chrome" />
<option id="op4" value="Opera" />
<option id="op5" value="Safari" />
</datalist>