A 2-2 draw with Swansea City on Saturday meant the Carrow Road club remain in trouble and could be just two points clear of the relegation zone depending on results on Sunday.
And defender Turner confesses Norwich are aware of their fans' nerves, which were particularly apparent as they made a slow start against Swansea.
He told Sky Sports: "We could feel a bit of tension from the crowd, especially in the first half. We were saying to each other, 'ignore it and stick to the game plan'.
"I think we did that in the second half and played a lot better and we were disappointed not to win the game."
Swansea, who arrived at Carrow Road having suffered three successive Premier League defeats, had dominated the opening half-an-hour and took a deserved lead through Michu.
Norwich responded courtesy of Robert Snodgrass and Turner either side of half-time but Luke Moore then earned a share of the points.
Goalscorer Turner was pleased to have recovered from Norwich's poor opening to the match but was equally annoyed to then lose the lead.
The centre-back said: "The way we started the game was very disappointing. We were not really at the races in the first half-an-hour.
"We managed to get back into the game and in the rest of the first half we played well.
"But in the second half we were better. With being one goal in front, we thought we could see the game through. But they still created a few chances and a draw is probably a fair result."