Dale conceded three first-half goals for the third game in succession on Saturday as they went down 4-2 at Aldershot - a fourth straight defeat.
Coleman invited fans along to his office on Monday for a "meet and greet" to air their views and the former Accrington manager insists he is the man to turn the Spotland club's fortunes around.
"I have an unshakeable belief in my own ability," he told the Manchester Evening News.
"I know I am a good manager and I know I have been through adverse times before and fought through.
"I certainly will not be hoping someone else will come and sort the problems out for me - I'll sort them out myself."
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