Roberto Mancini's men hammered rivals Manchester United 6-1 at Old Trafford in a sublime performance which was made possible by a Mario Balotelli double and later goals from Sergio Aguero, Edin Dzeko (two) and David Silva.
City have recently been described as United's 'noisy neighbours' but today Richards feels the Etihad Stadium club really flexed their muscle.
"People call us the noisy neighbours but here we are. We have a good set of lads and we want to show people what we can do," he said.
"I think we did that today. It's what dreams are made of. We all know how good United are and how good they are at home. But they know about our attacking force - Balotelli, Dzeko, Aguero, Silva.
"To come to Old Trafford and win gives confidence, especially the way we won. We'll only go forward now."
But Richards did admit there was disbelief at the scoreline as City inflicted United's first home loss in the league in 26 matches.
"I'm still gobsmacked to be honest. To come here and win 6-1 in unbelievable," he added.
"They had 10 men so you have to let them off a bit but in the first half we defended well and took the chance when it came."