Clare are facing a relegation battle in the final rounds of the National Football League.
A fourth consecutive defeat in Division Two, coming at the hands of Cork, leaves the Banner with just two points from five games, and sitting second from bottom on the standings.
Clare led the Rebels by 1-4 to 1-3 at half time in Cusack Park, but were outscored heavily in the second period to lose by 3-10 to 1-8.
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Manager Colm Collins admits their second half showing was not at the standard required.
Elsewhere in Division Two, Derry left it late before beating Dublin, Louth overcame Kildare while Limerick and Meath shared the points.
