Roberto Martinez's side outplayed City for long periods on Wednesday night but lost 1-0.
And Richards insists there will be no complacency when they meet again on May 11.
"It has given us a wake-up call," he said. "I think they were better than the whole team expected. They seem to know that system inside out.
"There were runners coming from everywhere. We will learn from that and make sure we are ready for the final."