The former Hull City man received his marching orders for serious foul play and was initially handed a three-match suspension.
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He was sent off following an aerial clash with England midfielder Gareth Barry during the 4-3 defeat.
Steve Bruce and the Black Cats management felt the initial ban was excessive and under a new regulation to seek to limit the disciplinary consequences, they appealed.
However, after the FA's consideration, it was viewed that the ban was fair and just.
They have now utilised their discretion to increase the penalty to four games, much to the club's frustration.
Bruce has also been asked to come forward and explain his post-match comments following Turner's dismissal.
A club spokesperson said: "The club is very disappointed with the decision on this occasion."