Shaw sensed out on the pitch that he and his teammates had a greater desire to win than a City side sat comfortably in second place in the table with no chance of catching runaway leaders Liverpool.
"I think it was so important, not just the points but the magnitude of the game and how big it is to everyone in this city," said Shaw. "I think if you look at it, maybe we wanted it more. I felt like we wanted it more. I'm very happy and proud of the way the team played.
"The fans were amazing today and it helps us even more when they're like that. The last few years they've had very disappointing results against Man City at home. Away we've been good, but at home we've struggled.
"You just smile when you come off the pitch, the way they're singing makes us all very happy. We're glad that we can get them singing like that with an amazing result like this."