United's assistant manager Carlos Queiroz had said after the 2-1 defeat that a number of his side's players had produced below-par performances because they were tired from midweek international friendlies.
"It was an amazing day. City had not won there for 34 years, so to be part of a team to manage it is phenomenal," Richards said.
"The City players were really up for the game. We wanted to show it was not only United who were turning up and that we had quality as well.
"The last thing Sven-Goran Eriksson had said before we went out at Old Trafford was 'don't be afraid' and he told us that we were better than Manchester United so we had nothing to worry about.
"Apparently, United win a huge percentage of their games in the last 20 minutes of the match. We were warned about that - and not to think we had won when it got to that stage.
"We were disappointed to concede a goal at the end but that did not matter when the final whistle went. It was the best moment of my club career."
He continued: "I have heard that United have blamed the defeat on player fatigue but I do not think that is a valid excuse.
"I may not have played for England last week but I had to go through the same as their players and train twice a day. It wasn't just United's players who did it, we all did.
"Plus England were at home. Many other players at City were away playing abroad so they had flights to contend with too."