Norwich have just one away win this season, but have recorded an impressive nine clean sheets from 29 Premier League matches to sit 14th in the table, three points clear of Sunderland and nine away from the relegation zone.
Securing safety is the priority for the Canaries.
"There's going to be twists and turns between now and the end of the season," Turner said. "We play Sunderland, who are below us, and then we play Wigan, who are in the bottom three at the moment.
"We've got big games coming up and I'm sure if we can get through those games in a decent position then we'll be confident."
Turner, who made 77 appearances in three years for the Black Cats before moving to Carrow Road last summer, has combined impressively with Sebastien Bassong in the centre of defence.
The 29-year-old is keen to enhance the Canaries' miserly streak.
"We've been pleased with the amount of clean sheets we've kept," he said. "That's something we're proud of. If we can keep a few more between now and the end of the season it will put us in a good position.
"Bass (Bassong) has been brilliant this year for us. An experienced player in this league, he's a good defender and it's been nice to play alongside him and keep as many clean sheets as we have done.
"It's obviously a team effort keeping a clean sheet, but it's very pleasing from a back four point of view to keep that many."