The 19-year-old was lifted off the pitch on a stretcher after being placed in a neck brace following an innocuous challenge with Matty Phillips.
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Targett's injury came in the 21st minute and delayed play for a considerable amount of time, but when the game resumed Mane continued to threaten and stung the hands of Green with a low drive after stepping off the wing.
In the 32nd minute, Mane was presented with his third opening of the half and again forced Green into a save.
From the resulting corner, Jose Fonte rattled the crossbar with a towering header as QPR struggled to half time with their clean sheet intact.