Recovering money that went to wrong account

What avenues are available to recover money that was sent to a wrong account?

I mistakenly gave someone a wrong account number to send money to me. As the wrong account is in the same bank (same BSB) I was hoping to get the money back. I asked the sender to contact their bank and request to recover it. However, after four weeks the sender notified me that their request to recover the payment was not successful. Message received from their bank as follows:

‘We refer to your request to recover the mistaken payment stated above. We wish to advise you that we were unsuccessful at our attempt to recover the funds on your behalf.
Under the Privacy Act we are unable to disclose any further information in relation to the recipient of the funds.
ANZ now considers this matter as finalised.
This email is automatically generated. Please do not reply to this email.’

Is there anything I could do to recover the lost money? Appreciate your advice.