Roberto Martinez's men succumbed to a 1-0 loss at the hands of struggling Sunderland on Thursday, falling just two games short of going a calendar year unbeaten at Goodison Park.
But captain Jagielka feels the club's failure to reach that milestone will now relieve some of the pressure.
"Maybe that's a little monkey off our backs and we can go out and play well on Sunday (against Southampton), get those three points and climb back up the table," he told the club's official website.
Everton will be without suspended duo Tim Howard and Gareth Barry against Mauricio Pochettino's charges, but Jagielka feels the squad has strength in depth.
"It's pretty simple," Jagielka added. "Joel (Robles) will obviously come in for T-How. He's been waiting for his chance and he's played well in some of the cup games.
"The manager will then decide what he'll do with the midfield, how he'll rejig that.
"But we've got a decent squad and some good players to come in, some fresh players as well - which is obviously important over this period - so hopefully they can come in, freshen up the squad, and we can put in a good performance on Sunday."
