The defeat against the Red Devils was their fourth in their last eight games in all competitions, casting doubt over Maurizio Sarri's long term future in the dugout at the London club.
First up, Sarri's men will look to protect their 2-1 aggregate lead over Malmo on Thursday night as they look to advance to the last 16 of the Europa League.
But, as their club captain has highlighted, lifting the Carabao Cup this Sunday is the main priority to help bring the fans back on side and keep their season on track.
"Hopefully we can have a good nine days. It's the whole season," Azpilicueta told Chelsea TV.
"We know that a trophy in the middle is everything, to bring the fans back to Wembley with the spirit to get the Cup."
Azpilicueta also lamented his side's inability in front of goal against Manchester United, and hopes they will be able to rectify that in their upcoming games.
Sarri’s men had just two shots on target against Ole Gunnar Solskjaer’s side even with new signing Gonzalo Higuain leading their attack.
"We didn't put Manchester in difficulties even at 2-0 down," he added. "We were not very good in the final metres, so we paid [for] that. And at the end we couldn't score."
The Blues also recently suffered a humiliating 6-0 defeat to Pep Guardiola’s side and managed just four shots on target throughout that entire game as well.
The west London outfit will need to up that tally if they are to claim the first trophy of the season over City on Sunday.
Sarri is still in his first season as the manager of the Stamford Bridge club, and is under contract until at least 2021.