Warner went undrafted from the top price bracket of £125,000 ($A215,000), joining Finch, Chris Gayle, Tabraiz Shamsi, Babar Azam and Mohammad Amir as other big names to go unsold.
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It was not all bad news for the Australian men though, with spinner Adam Zampa off to Cardiff as an overseas signing while Glenn Maxwell has been retained by London Spirit.
Maxwell will be joined at Spirit by fellow Australian Riley Meredith, who was picked up for $A129,000.
Elsewhere, Hilton Cartwright was signed by the Oval Invincibles while West Indies all-rounder Kieron Pollard was taken with the first pick and highest possible price of $A215,000.
Birmingham Phoenix spent $A215,000 on wicketkeeper-batter Matthew Wade with Kane Richardson taking their other overseas spot.
Marcus Stoinis has been retained by the Southern Brave while Sean Abbott was snapped up as an overseas pick for Manchester Originals.
On the women’s side, World Cup heroes Alana King, Beth Mooney, Rachael Haynes, Meg Lanning, Tahlia McGrath and Megan Schutt were all snapped up.
Australian World Cup skipper Lanning and spinner King were picked up by the Trent Rockets.
London Spirit picked up Mooney and Schutt while Haynes and fellow Australian Annabel Sutherland were taken by Welsh Fire.
In other news, Southern Brave made a few moves, with the most significant signing coming in the form of Aussie all-rounder McGrath.
Elsewhere, Sophie Molineux may have missed the World Cup with injury but she has been snapped up by Birmingham Phoenix, joining Ellyse Perry (retained).
Alyssa Healy, meanwhile, like Perry had already been retained by Northern Superchargers.