France international Samir Nasri put the visitors ahead in the 23rd minute before Dutch striker Siem de Jong levelled for Frank de Boer’s side just before half-time.
Ajax defender Niklas Moisander completed the home side’s comeback with a timely header in the 57th minute, prompting Mancini to switch to a 3-5-2 formation.
The change proved disastrous as the Eredivisie winners ruthlessly exploited a visibly confused Citizens rearguard, and Christian Eriksen added a third to seal the victory.
“We’ve been beaten by a very good Ajax team but we should have done much better,” said Richards.
“When we went a goal up in the first-half they were probably the better team, but in the second period, we just crumbled.
“We are all very disappointed with the way we performed.”
He added: “I mean it [3-5-2] is something that we haven’t worked on a lot.
“We’re used to a straight back four. We’ve gone to a back five twice and we’ve conceded this season.
“But the manager likes it, and if we want to do well in Europe, we’re going to have to work on it a bit more. The players just want to play.
“It’s a hard system because we’re not used to it and the players prefer a 4-4-2. But he’s the manager and we’ll do what he says.”
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