Manchester United have now gone 14 home matches in all competitions without keeping a clean sheet, which is their worst run of conceding at Old Trafford since a 21-game run between April 1958 and March 1959.
An own goal from Eric Bailly and close-range Bernardo Silva finish saw Manchester City record a 2-0 win in the Manchester derby on Saturday afternoon.
The Red Devils are now without a victory in the league at Old Trafford since September 11, losing three of their last four against Aston Villa, Liverpool and Man City.
The team's failure to produce a shutout in the derby means that they are without a clean sheet in their last 14 home matches in all competitions, which is their worst run since 1959.
Man United's last clean sheet at Old Trafford came against Granada in the Europa League back in April, when Ole Gunnar Solskjaer's side managed to record a 2-0 victory.
Despite a disappointing run of form, Solskjaer said after Saturday's defeat to Man City that he was not fearful of losing his job with the 20-time English champions.