The Reds needed to win and also for Jeju United not to gain any points from a simultaneous fixture.
But coupled with Adelaide's defeat, South Korea's Jeju downed Gamba Osaka 2-0 to advance to the ACL round of 16.
Adelaide finished third in the group, some five points shy of Jeju, after an Asian campaign which returned one win, three draws and three losses.
But before 6,797 spectators at Coopers Stadium, the Reds bossed a second-string Jiangsu outfit - the visitors leaving their stars at home, having already sewn up top spot in the group.
But a wayward Adelaide couldn't land a punch despite basking in 71 per cent possession and recording 20 shots to six - including nine to one in the opening half.
The Reds fluffed a succession of chances - Riley McGree, Nikola Mileusnic, Sergio Cirio, Baba Diawara and Kim Jae-sung all sprayed shots wide, while Diawara also hit the post with a header.
McGree also had an early gilt-edged chance denied when, just five metres from goal but on his non-preferred right foot, with his shot superbly saved by Jiansgu goalkeeper Jiang Hao.
The visitors, with imports Alex Teixeira and Roger Martinez at home and missing Brazilian international Ramires because of suspension, relied exclusively on counter-attacks.
And, on 81 minutes, they made Adelaide pay for their lack of finishing polish - a common theme in the Reds' disappointing domestic campaign - when Ji Xiang scored with a sweet left-footer from 15 metres out.
Adelaide's focus now turns to signings - they have 16 players about to fall off contract and a coach, Guillermo Amor, who is weighing up his future.