The certificate of your backend will usually not be automatically available to the vSphere Client server, unless it is signed by a trusted authority.
You don't need the certificate installed. What you can do, instead, is pass known thumbprints to the Apache HTTP client (or whatever other library you are using to send the requests).
The actual thumbprint of your backend should be registered in your vCenter extension - add a new record under vim.ExtensionManager.extensionList[your-extension].server and populate the serverThumbprint field. If you're providing the client plugin from the same server, the thumbprint should be populated already. For more details on the VC ExtensionManager API see http://pubs.vmware.com/vsphere-65/index.jsp#com.vmware.wssdk.apiref.doc/vim.ExtensionManager.html.
