City are top of the Championship after beating Ipswich and winning at Barnsley on Saturday but no-one is getting carried away.
"Look what happened last season," said Coleman to the CT. "After 10 games we were sixth and I heard people saying, 'This is it,' but then it bit us on the backside.
"It's very hard to calm people down when things are going well, but it's vital that we stay level-headed.
"This is a very tough division and although we've won two games while Barnsley have drawn one and lost one, we're both in for a tough season.
"A few results either way can make all the difference because there's a very fine line between teams in the top half pushing for the top six and teams trying to stay out of the bottom six.
"And just as we won't start panicking if we lose one or two games, we won't get carried away because we've won a couple.
"I can't do anything about what people say or write, but we won't pay any attention to outside influences.
"I don't care what's being said outside my little group - the players, the chairman and the board - we will stay level headed.
"Nobody here will be talking nonsense, we'll keep things nice and quiet and get on with our business."
Pictures from the Barnsley game can be found here:
http://footymad.sportbox.tv/photos/imagepopup.php?sport_id=1&team_id=6
See the goals (uk only) http://news.bbc.co.uk/sport1/hi/football/eng_div_1/8204376.stm