I have just set up my mail server and added a couple of email accounts. I've verified my domain and added the mx records with my registrar (namecheap.com)

What I'm trying to do is to be able to send email from my domain through Gmail. 

In Google I have added the account and have set up gmail to send through zoho's smtp server: smpt.zoho.com

That authenticates without any issue, I was able to verify the account, and the email address is now available to be used in gmail. However, when I do try and send any emails I get the error: 

Delivery to the following recipient failed permanently:

      dave@[omitted].com

Technical details of permanent failure:
Google tried to deliver your message, but it was rejected by the relay  smtp.zoho.com  by  smtp.zoho.com . [74.201.154.90].

The error that the other server returned was:
553 Relaying disallowed

-------------------

I am using my admin account to authenticate with google, but I'm trying to send with one of my other email addresses on the same domain (that email address has been added in my zoho, already as well.)

Did I just not complete the server setup? Not sure what I'm doing wrong.