The Toffees are now two points adrift of Tottenham in fifth and Chelsea in fourth, but have played a game more than Spurs and two more than the Stamford Bridge side.
David Moyes' men finish the campaign with games against Sunderland, Fulham, Liverpool, West Ham and Chelsea and are the outsiders to claim a place among Europe's elite.
But England international Jagielka, who was named man-of-the-match after an impressive display, insists they will fight on until the end of the season.
"It's not over," Jagielka told Sky Sports. "I said before that we need favours from other teams and that will still be the case.
"If we had lost tonight it would have been an even bigger hurdle for us to get over. We'll keep battling on. As long as we're in there for as long as possible we've had a good season.
"It was quite an exciting game, especially in the first half. I'm sure it was a good game other than the lack of goals.
"We looked a little bit edgy. We both gave each other quite a lot of respect because of the run of form that both teams are in, we've both got a lot to play for.
"We knew it would be hard coming down here. We've struggled to get points at the Emirates and it was nice to come away with a clean sheet."