The newly promoted side were reduced to 10 men when Nigeria international Taiwo Awoniyi was shown a red card in the 53rd minute.
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The defeat means Coventry have lost each of their opening four matches without scoring, making them only the fifth team in English top-flight history to endure such a start.
They have now joined Derby County, Stoke City, Preston North End and Crystal Palace on the unwanted list.
Derby first suffered the fate in 1899-1900, while Stoke repeated it in 1906-07. Preston followed in 1924-25, before Crystal Palace became the most recent team in 2017-18.