Saturday's 1-0 victory over Stoke courtesy of Kevin Mirallas' 70-yard run and finish built on the win over defending Barclays Premier League champions Manchester City before the international break.
Since their dismal FA Cup quarter-final exit at home to struggling Wigan the response has been typical of the Toffees, bouncing back with a maximum six points.
That has re-ignited their top four challenge, now only four points adrift, and even though Arsenal and current incumbents Chelsea have bigger squads, more star players and have spent more money, Jagielka insists Everton can still match them.
"We'd like to think we can prolong the chase as long as possible," said the centre-back, returning after missing three matches with a gashed ankle.
"If we're going into the final game of the season still in with a chance of Champions League football then we have to look at that as a fantastic season.
"Unfortunately for us it is a season when five or six teams at the top rather than two or three are performing well.
"It seems like Spurs have played well again and won, Arsenal have so everyone seems to be desperate for that fourth spot and we're desperate to be in there as long as possible.
"You can only work with what you are given and I am sure the manager would have loved to have had a lot of money in the January window when we were up there in a better position (they were in the top four in late December) than we are now.
"But it is hard to wish for things which are not going to happen.
"The manager has got the players he's got, he has done the best he has with the players he has got in and when I look around the dressing room I'm happy with the players we have trying to get us into fourth spot.
"We are - as far as spending is concerned - a little bit below the other teams but I am sure they won't look forward to playing us as much as we are looking forward to playing them."
Third-placed Tottenham will find that out next weekend when Everton visit White Hart Lane and Arsenal also less than a fortnight later.
Those two matches are likely to be definitive in the Toffees' chase to qualify for Europe's elite club competition for only the second time.
The doom and gloom which emanated from Goodison Park after their cup failure has quickly been dispelled and Jagielka felt that defeat may have actually helped re-focus the minds.
"One of our worst performances of the season came in the most important game up to that point but I don't think the lads in the changing room ever need a kick up the bum," he added.
"We don't have too many people who don't turn up on a regular basis.
"But maybe it was a general reminder that possibly before we play the good stuff we make sure we stick to our guns and get the dirty side out of the way: the running, the rough and tumble, tackles.
"Maybe for the Wigan game we turned up and didn't do those first and foremost and got punished."
If Everton were expecting some rough and tumble against Stoke they were happily mistaken as the woefully out-of-sorts Potters, now with only one win in 12 league matches, rarely threatened.
However, the standard struggled to rise above mediocre and Mirallas' goal shone like a beacon through the ordinariness.
Tim Howard punched clear to the Belgium international midway inside his own half and, after squeezing past Steven Nzonzi, set off on a blistering run leaving defenders trailing in his wake to score past Asmir Begovic.
Stoke are just four points above the relegation zone and Saturday was the 14th league match this season they have failed to score.
"We need to get some points and we need to score some goals, which has been our problem all season," said manager Tony Pulis.
"But we created enough chances at Everton to have at least scored a couple of goals and that is what is probably the biggest worry.
"We have had a fantastic five and a half years in the Premier League and we are struggling for that little break.
"Never mind whether you get it quickly or late on, we need 40 points to stay in there and that is what we have to do."