The Pilgrims are now five points behind sixth-placed Crystal Palace with three matches remaining, and Sturrock concedes that is too big a gap to make up.
He said: "While it's mathematically possible we'll still give it a go. But really, we needed the win on Monday.
"The first goal, it sounds a strange thing for a manager to say, came too early. The goal changed our mental approach and it was a disappointing performance."
Sheffield Wednesday manager Brian Laws remains confident his side will avoid the drop after the Owls battled back to take a point.
He said: "It's going to go to the wire, but the players have a lot of belief in their ability and a lot of confidence.
"It's all about keeping your nerve. Everyone is going to be nervy down at the bottom.