With the credit crunch starting to bite and even Prime Minister Gordon Brown talking about recession, City's crowds have dropped this season and Tuesday night's attendance of 14,621 was the lowest for a home League game since the club moved to the Ricoh Arena in August 2005.
"You cannot underestimate just how important a vocal and noisy crowd can be to the confidence of a team and we saw that at Wolves. The fans were magnificent," Coleman said to the club's marketing department.
"The fans play a very, very big part and I hope they realise that. Sometimes that atmosphere can get a bit lost at the Ricoh because it's such a big stadium.
"But it's another important game against Derby on Saturday and I hope the fans can be just as noisy at the Ricoh as they were on the road the weekend before."