City is left bottom of Group D after defeat to the Eredivisie title holders, with the right back admitting his side has not practiced much with a three-man defense
Mancini made the switch, with scores level, in the second half but promptly saw his side concede twice in 10 minutes and now sees his team rooted to the bottom of Group D.
City has switched to a 3-5-2 system on numerous occasions this season, but Richards revealed that the players are not comfortable playing in the formation, due to a lack of practice in training.
"It is something that we've not worked on a lot," he told Sky Sports. "We're used to a straight four and it's twice we've gone to a back five and conceded, but the manager likes it and if we want to do well we're going to have to work on it a little bit more.
"The players just want to play. It's a hard system because we're not used to it but I think the players prefer a 4-4-2 but he's the manager and we do what he says."
Richards praised Ajax's performance but admitted that City was expecting to win in the Dutch capital.
Defeat leaves City able to reach a maximum of 10 points, the same total that it finished on last season when the English club was eliminated from the competition at the group stage.
"I think we got beat by a very good Ajax side tonight. First half, when we went 1-0 up, they were probably the better team," Richards said. "But in the second half we just crumbled. Very disappointed with the lads' performance tonight."