"The board would like to place on record their thanks for his efforts over two and a half years.
"We will not be rushed into finding a successor and the board will explore every avenue to appoint the right manager to take Coventry City forward."
Coleman, who made over 30 appearances for Wales, had a playing career that included stints at Swansea, Crystal Palace, Blackburn and Fulham.
However, he was forced to hang up his boots in 2002 after failing to recover fully from a serious car crash nearly two years earlier.
He was appointed manager of Fulham in 2003 but parted company with the London club in 2007 before having a stint in charge of Spanish side Real Sociedad.
I'm doing something wrong - I am - but it's not all just me making mistakes as a manager
Chris Coleman after Sunday's defeat
After Sunday's defeat, Coleman said: "There were no positives to that, not one. It was an embarrassing end to the season for us. It was the worst possible way to go out.
"I'm doing something wrong - I am - but it's not all just me making mistakes as a manager. I've got a great staff who work very hard but we need to make changes and that was evident in the game.
"It is not good enough and I apologise. The players went out after the game to say thank you to the supporters but if I had been a supporter, I would have gone. In fact, I would have gone before the end."
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