The club currently occupy 11th spot in the Premier League with five matches to play, but Turner wants a 'strong' finish to the season.
"We want to finish the season strongly, we don't want to let it just fizzle out," the 28-year-old told The Echo.
"I don't think we have to set ourselves a points target or anything like that. But we just want to win more games and finish what's been a good season after a bad start.
"If we can get a few wins and put a smile on the fans' faces, then going into next season we can look forward to it."
Turner joined Sunderland from Hull City in 2009.