United lost 3-2 at home to a fearless and skilful Athletic Bilbao, their second successive European defeat at Old Trafford, in the first leg of their round-of-16 tie.
Central defender Xandao scored with a cheeky backheel to give Sporting a 1-0 win over City in Lisbon, ending the Premier League leaders' run of six straight wins.
A Luuk de Jong penalty gave Twente Enschede a 1-0 win at home to Schalke 04 and Olympiakos Piraeus won by the same score away to Ukraine's Metalist Kharkiv thanks to David Fuster's second-half strike, the Greek champions' ninth successive win in all competitions.
"We were well beaten, they were the better team," manager Sir Alex Ferguson said in a television interview.
"Our defending wasn't very good tonight, our attacking play was very open at times."
The equaliser came in the 41st minute when a well-worked move ended with Fernando Llorente ghosting in to meet Markel Susaeta's chipped cross with a powerful low header.
Athletic's fans outsung the home supporters and were given more to celebrate in the 71st minute with a superbly worked move which ended with Ander Herrera flicking the ball over the United rearguard for Oscar De Marcos to hook the ball in with a first time shot.
Athletic swiftly attacked and De Marcos' shot was parried by David de Gea. Although there seemed to be no Athletic player in sight, Rafael was caught napping and the always dangerous Iker Muniain stole in to fire the ball into the roof to net.
"I don't know how you describe the third goal," said Ferguson.
