Richards powered home David Silva's second-half corner to settle a tense quarter-final with Reading at Eastlands on Sunday.
It earned City a trip to Wembley, where they will face neighbours Manchester United on April 16 or 17, ending a three-decade wait for a last four appearance in the world's oldest domestic cup competition.
"It felt amazing," the 22-year-old told www.mcfc.co.uk. "To come through the youth academy and get us so far in the competition is an unbelievable feeling.
"We have United in the semis, which makes it more special. We can't wait."