City threw away a 2-0 half time lead to lose 3-2 at Wembley with Nani sealing the victory for Sir Alex Ferguson's side in injury time.
Despite the uncertainty over Carlos Tevez's future, the Blues are one of the favourites to challenge for the Premier League title this season.
The signing of Sergio Aguero from Atletico Madrid has given supporters more hope that they can compete at the top of the table.
But, speaking to the Manchester Evening News, Richards says he isn't getting carried away.
He said: "As much as it pains me to say it, United were the better team.
"It's an outstanding time to be at City with the way things are going. It's exciting. But it was a bit of a wake-up call for us.
"People know what we can do but maybe we got a little bit ahead of ourselves."
Manchester City begin their Premier League campaign against new-boys Swansea City next Monday.
Joleon Lescott, who scored the opening goal on Sunday, says the defeat won't derail their preparations.
The defender said: "We would have liked to win it. But no disrespect, our season is bigger than the Community Shield.
"It won't affect us negatively. We can take a defeat on the chin and we won't dwell on it, like we won't dwell on our victories too much.
"We had a great season last year but this is a new season. We've got new signings and once everyone is back together and firing on all cylinders, I'm sure we'll be there or there abouts again.
"It might help us keep our feet on the ground because we're not at the level we think.
"There's a long way to go. The game was important but it's not the be-all and end-all of our season."