Goals from in-form striker Ayegbeni Yakubu and prolific defender Joleon Lescott were enough to dispatch a City side which showed no changes from the team which had beaten Manchester United last time out.
And Jagielka, who shone at the back for the Champions League chasing Toffees, remains optimistic after his side reclaimed fourth with three valuable points.
"It was a massive result, looking how tight the table is and coming to a place like here, where they've been fantastic at home," he told Setanta Sports 1.
"Obviously the second half they put pressure on us but we have some decent defenders and others willing to muck in," said the former Sheffield United man.
"It's important to keep fourth place if we can and if we can finish there it will have been a massive season for us.
"Every point from now until the end of the season matters; it is six-pointers every week.
"If we can keep our performances like tonight we should be there or thereabouts."