[SalesForce] apex:inputText required=”true” doesn’t work as in the documentation

I want to make an inputText field's attribute required="true" on the VF page and display the error message : Error: You must enter a value (Note: I do not want to use an InputField here)

When I click on the submit button, this doesn't show me the inline error message.

Please see the below code, and can some one explain what am I doing wrong here?

<apex:page sidebar="false" showHeader="false" id="page" standardController="Case" extensions="MyControllerExt">
<div>
    <apex:form styleClass="form-horizontal" id="form">
        <div class="requiredInput">
            <div class="requiredBlock"></div>
            <apex:inputText value="{!myCustomVar}" id="LastName" label="LastName" required="true" />
        </div>
        <!-- Submit From -->
        <apex:commandButton id="btn2" styleclass="btn btn-lg btn detail" rerender="form" value="Submit" action="{!submitAction}" />
    </apex:form>
</div>

And this is what the document say about the required true attribute;

required -> Boolean -> A Boolean value that specifies whether this field is a required field. If set to true, the user must specify a value for this field. If not selected, this value defaults to false.