Some City supporters are understood to have been were deeply unhappy after the defeat to Swansea but Coleman said to the CT: "If we can take seven points from the next four games, I'll be delighted.
"I don't know if it happens at every club but when you lose one game here you can smell the panic. "It's always, 'Oh no, here we go again,' and I think that's bizarre.
"I've already had a letter from one supporter saying that the Swansea game was the worst football he'd ever seen in his life and he's not coming back.
"I might send him a reply saying 'good, don't come back' - I don't want people like that supporting us."