Roberto Martinez's side head to fourth tier side Carlisle United on Sunday for a fourth round FA Cup tie and Jagielka said they need to give the supporters something to cheer about after their latest setback.
"We have another cup game at the weekend and so we have got to try and put some sort of run together to give them something to get their teeth into for the remainder of the season," the England international told British media.
"It is important that we get our heads up. The role of all of the senior people around the dressing room is to get everyone back up, it's another decent distance for them to go. I wouldn't say the FA Cup can save the season but it can make the season.
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"Things aren't going so well in the league so a good run in the FA Cup can make things a lot happier, similar to what the League Cup has done but there is only one way to do and it's going to Carlisle and getting a good result."
Everton have not won any silverware since lifting the FA Cup in 1995.
(Reporting by Shravanth Vijayakumar in Bengaluru; editing by Amlan Chakraborty)
