The Citizens were reduced to 10 men after Phil Foden’s 23rd-minute dismissal, leaving them facing a difficult task in the derby.
Anderson was one of City’s standout performers, earning Player of the Match honours after an impressive midfield display.
Despite the individual recognition, the summer signing insisted the victory was a collective effort.
“We are now! (Kings of Manchester). We always knew it would be a tough game,” he told City website.
“Losing Phil at the start wasn’t good for us but we said at half time it would make us feel better to win. We took the three points.
“It (red card) gives you more motivation to go and get the points. It was really tough for us. We had to run more and fight more. We all shone to a man and we were brilliant.
“All of our midfield do (relish these games). Me and Enzo (Fernández) love to fight, tackle and get on the ball and play. We gave it our all today and everyone was brilliant.”