I am trying to search Contacts details from database using lastname field and dsiplay the table in VF page.  I am able to search and display the existing records in the page but if the record(Contact) is not in the database, I need to display the error message: "Contact could not found".  This is where i am looking for some help.
Code for my controller is:

public with sharing class ContactSearchController
{
    // Global variables
         public List<Contact> contacts{get;set;}
         public String searchString{get;set;}
         
   // Constructor for stand alone page
   
            
         public ContactSearchController()
         {
          searchString = '';
          doSearch();
         }
         
    // Methods for getting List of Contacts
       
         public void doSearch()     
         {
            String queryString = '';
            
            if(searchString!= null)
            {
                queryString = '%'+searchString+'%';
            
                contacts = [SELECT id, name, accountId, email, phone 
                            FROM contact C
                            WHERE lastname LIKE :queryString
                            LIMIT 10];
            
           }
           else
           {
             ApexPages.addMessage(new ApexPages.Message(ApexPages.Severity.ERROR, 'Contact could not found!')); 
                        
         }
        
 }        
}

My VF page is :
<apex:page controller="ContactSearchController" >
<apex:form >

<!-- actionFunction is for calling Controller's method -->
<apex:actionFunction action="{!doSearch}" name="apexdoSearch" reRender="myData,errors"/>

<!-- Filter Section -->
     <label> <b>Filter by Last Name:</b></label>
       <apex:inputText value="{!searchString}" onkeyup="apexdoSearch()"/>
       <br></BR>
       
  

 <!-- My Page Block -->
  <apex:pageBlock title="Find Customer" id="myData">
  <apex:pageMessages id="errors"/>
  <apex:pageBlockTable value="{!contacts}" var="contact">
  <apex:column value="{!contact.name}"/>
  <apex:column value="{!contact.accountid}"/>
  <apex:column value="{!contact.email}"/>
  <apex:column value="{!contact.phone}"/>
  </apex:pageBlockTable>
  </apex:pageBlock>
  </apex:form>
</apex:page>