The Toffees are currently six points above the drop zone and are sitting in 12th place having won just the one of their last 10 Premier league games.
Their latest encounter was a 2-2 draw against bottom club Leicester City at Goodison Park on Sunday. Roberto Martinez has said he isn't looking too closely at the league table yet, but Jagielka seems aware of their predicament according to the Daily Express.
He said: "As much as we are aware of the predicament we are in, we don't see ourselves as being in the relegation battle at the moment," said the defender, who experienced dropping out of the top division with Sheffield United in 2007.
"It wouldn't take a lot to put us in there - a few bad results for us, a few good results for the teams around us and we will drop into that battle.
"But as it stands at the moment if we keep performing okay, get back to keeping clean sheets and keep grinding out results, then hopefully the league will take care of itself.
"Then we can look forward to the European games because there is something special to go for there."
It's quite a contrast from last season when Everton finished with a Premier League club record total of 72 points. There is no chance of Everton achieving that now but they are desperately in need of some form on the domestic front between now and the end of the season.