Power to the data centre, which is a Pipe Networks' peering exchange, was cut at about 2pm.
It was restored about four hours later according to ISP service disruption reports but Internet forum users continued to report issues into the night.
It affected ISPs including Internode, iiNet and Westnet.
A spokesperson for Primus could not be reached for comment.
Inundated with complaints, ISPs and their customers vented their frustration on forums and to iTnews.
"We haven't had a detailed report yet on the circumstances [surrounding the failure]," Greg Bader, CTO of iiNet, told iTnews.
"Once we receive the report this afternoon we'll sit down as a group and look at what steps we can take to mitigate the risk of it happening again.
"No one is interested in pointing fingers - we just want to get services back up, but the situation isn't ideal. We expect our data centres to be able to withstand power failures," Bader said.
Internode re-routed interstate and some local traffic through a back-up data centre in Melbourne, said its managing director, Simon Hackett.
"Had we not had that dual data centre strategy, there would have been major service issues in other states as a result," Hackett said in a statement posted to Whirlpool.net.au.
"That did indeed happen for some other providers who had only that site in Melbourne as their Melbourne access point."
He told iTnews he would wait on the post-incident report before deciding next steps.
"We do of course expect (and we normally obtain) better results during loss of external power than that from all of our data centre providers nationally," Hackett said.
"We're awaiting a (report) from Primus before deciding what additional steps to take in response to this outage, based on understanding what Primus themselves intend to do in order to mitigate against the potential for a recurrence.
"The Primus data centre concerned is a major communications site for much of the industry, so you can rest assured that we'll be ensuring, with Primus, that this doesn't become a habit. We don't expect that it will."
Read on to page two for the latest on the cause of the failure.