City are currently in 18th place with two matches remaining after dropping into the bottom three following five successive defeats.
They now face Chelsea at Stamford Bridge on Sunday followed by another tough game against Arsenal at Carrow Road on the final day of the season.
With fellow relegation candidates Sunderland, Cardiff and Fulham all playing 24 hours before Norwich kick off at Chelsea, Turner and his team-mates will all be listening out for updates.
"I'm sure when we are travelling down we will be aware of the results going on," he said.
"It is out of our hands so we will be aware of the results coming in and obviously we need teams to do us favours but when it comes to it on Sunday we need to make sure we do ourselves justice.
"Last weekend, Hull getting the draw at Fulham was a lift to us and then we disappointed going out there ourselves. It is about what we do, first and foremost, because if we don't do the job there is no point other teams doing us favours."
Norwich lost 4-0 at Manchester United last weekend and Turner admits it will be a tough task to return to winning ways by beating Chelsea.
He said. "You need a great team performance, everyone has to play well individually and as a team you have got to be spot on and hopefully we can do that.
"We have been working hard all week in training to go there with a game plan, which is how we have got results there in the past. It is a very tough place to go and a tough team to play against, but we will be ready and hopefully we can put in a good performance."
Turner insists the Norwich players have got the result at Old Trafford out of their system and are ready to go again on Sunday.
"We have got back on the training ground and worked hard every day and are fully focused on the next game at Chelsea," he said.
"It was something we had to put behind us quite quickly. We know there are two games left and we have to put our all into them. We can't mope about thinking about getting beaten at Manchester United.
"I think we will need something from both games - that is where we are. We go into the Chelsea game to try to get something and take it from there.
"From the players' point of view we are fighting for our lives and we will give it everything we have got and hopefully it will be enough."
Watch Chelsea take on Norwich live on Sky Sports 1 at 4pm on Sunday.