You need to prevent default submit action if something is wrong
$(document).ready(function(){
$('form[id=Login_form]').submit(function(event){
var usernameTxt = $('#txt_username').val();
var passwordTxt = $('#txt_password').val();
if (usernameTxt =="" || passwordTxt =="") {
alert("username or password required !");
event.preventDefault(); //prevent default submit action
}
});
})