The Premier League leaders were knocked out of the domestic cup courtesy of the Reds, despite scoring two goals at Anfield.
A controversial moment in the game came when Richards was penalised in the penalty box for appearing to block a shot with his arm after the ball bounced off the defender's leg.
"I think the referee made a poor decision for the penalty," Richards told City TV. "It struck my foot and has gone on to my hand. I don't know what he expects me to do with that. But it was a decision. I won't say it has cost us but it has clearly played a massive part."
"Everyone goes on about respecting referees but it is decisions like that that are sometimes costing us. I give my full support to the referees but with those sort of decisions, unless you are 100% sure, you shouldn't really be giving them."
Liverpool will now face Cardiff City in the final of the Carling Cup while City resume focus on their Premier League campaign.