A 2-0 loss for Al-Sadd's compatriots, Al-Gharafa, against Iranian outfit Tractor FC meant Mancini's side clung on to eighth place in the western league phase standings to claim a spot in the knockout rounds.
Al-Sadd will take on table-toppers Al Hilal over two legs in early March in the next round, while Al Ittihad, who finished fourth in the standings, face off against Al Wahda from the United Arab Emirates.
Defending champions Al Ahli, also from Saudi Arabia, will play Al-Duhail from Qatar, with Tractor meeting UAE's Shabab Al-Ahli.
"Today was a very difficult game," said Al-Sadd goal scorer Rafa Mujica. "The first 20, 25 minutes were very bad for us. We conceded everything.
"But we only have to think about the next game. We are qualified. We will see in the next game."
Mancini's team needed to match or better the result recorded by Al-Gharafa but went two goals behind inside the opening 18 minutes when Houssem Aouar and Youssef En-Nesyri struck for the visitors.
A Pedro Miguel own goal in the 33rd minute compounded Al-Sadd's problems, although Mujica gave Al-Sadd a glimmer of hope seven minutes before the interval.
Stephane Keller restored Al Ittihad's three-goal cushion when he scored with a close-range finish in the 63rd minute as the Saudi side notched up their second comfortable win in a row.
Al-Gharafa's hopes were erased, however, when their Iranian visitors scored twice in the final 30 minutes to knock Pedro Martins' team out of the competition.
Mehdi Hashemnejad netted after the Al-Gharafa defence failed to clear in the 61st minute, and Amirhossein Hosseinzadeh's deflected effort into the top corner put the result beyond doubt with nine minutes remaining.
