"The use of the Cloud ... would incur significant unbudgeted costs to the ratepayer in terms of providing screens, security and other services."
Auckland Council's rough estimate for the cost was about $45,000. The city owned the screens, but they required installation.
Mr O'Riley said there was "no plan" to screen the free-to-air final at Auckland ratepayers' expense.
"It's important to note that the difference with this event and the RWC 2011 and CWC 2015 is that Auckland was a host city for these two events."
Those two Auckland-based World Cup events brought visitors to the region and pumped millions of dollars into the economy, which justified spending ratepayer funds on providing activities for fans.
This Sunday morning's Auckland Marathon was also a reason not to screen the Rugby World Cup final, because more than 12,000 people were expected to pack the waterfront for the race.
Mr O'Riley said the Cloud had been "well utilised" since the 2011 Rugby World Cup.
But the lack of a fanzone for this year's games has had All Blacks fans up in arms, with Herald readers writing to express disappointment.
Taxpayers shelled out $9.8 million in 2011 to build the Cloud, plus another $900,000 to buy two giant screens so they could be used in future. The screens, still owned by the council, have remained off during the 2015 tournament.
Aucklander Grant O'Sullivan said he could not fathom "the lack of judgment" shown by Ateed.
"The amenities are there and paid for by us and as our servants, the council should front up and screen this great event."
Taylor Oakes said there needed to be a place to watch the game in public as "it's the best way to send off six legends of the game".
Thomas Klaassen agreed: "The experience and atmosphere of being around hundreds or thousands of Kiwis supporting the same cause are second to none. Having experienced this four years ago, winning the Rugby World Cup whilst in my lounge just wouldn't be the same."
Other councils contacted by the Herald - including Whangarei, Hamilton, Tauranga, Napier, Palmerston North, New Plymouth, Wellington, Nelson, Christchurch, Dunedin and Invercargill - are also not holding any special events for Sunday's final at Twickenham.