The England defender feels his club side are good enough to finish in the top four of the Barclays Premier League, but knows a tough challenge lies ahead.
Everton maintained their top four aspirations with a comfortable 2-0 win over out-of-form Norwich at Goodison Park on Saturday.
The Toffees have impressed throughout the season and, just over halfway through the campaign, they look to be in a battle with Liverpool, Tottenham and Manchester United for fourth spot.
Jagielka said: "I think it is realistic and it is an aim, but it is going to be a very tough season with the amount of teams that are in there challenging.
"It's the same as before the game. We are in with a chance.
"Obviously quite a few of the teams around us have won again. That seems to be the way the league is going at the moment, but it is up to us to keep ourselves in the mix for as long as possible.
"With wins like this, and decent performances, we are still in the mix."
Hard-working Everton dominated the first hour of their contest against the Canaries and were rewarded with superb strikes from Gareth Barry and Kevin Mirallas.
Barry opened the scoring with a swerving long-range strike after 23 minutes before Mirallas made the scoreline more realistic with a fine free-kick after 59.
Norwich did stir into life in the latter stages, but Robert Snodgrass' header against a post was the closest they came as their slump continued.
Jagielka said: "It was a tough game, especially the last part of the second half.
"We had to hang in there and work that bit harder for a clean sheet.
"But two fantastic goals for us and it is nice to walk away with three points."
Victory wrapped up a good day for the Toffees, who completed the signing of former Celtic winger Aiden McGeady from Spartak Moscow before the game.
With Sylvain Distin, Gerard Deulofeu and Ross Barkley all absent, it also provided further evidence of the club's strength in depth this season.
Midfielder Barkley has a suspected broken toe and is due to undergo further assessment before the squad fly to Tenerife for a warm-weather training camp this week.
Jagielka said: "It says a lot if you think about the players who haven't been available.
"We still had a pretty decent bench as well. The squad is decent in numbers and hopefully we will get a few of those boys back as quickly as possible.
"It is going to be an interesting end to the season.
"There are obviously many teams that can go on fantastic runs, but if we can keep putting performances in we are not going to be far off."
It is starting to look tight at the bottom of the table and Norwich ended the weekend just two points above the relegation zone after a sixth league game without a win.
Attention now switches to next week's home clash against Hull with midfielder Bradley Johnson admitting Tuesday's FA Cup third-round replay against Fulham is a distraction.
Johnson said: "We are not looking at the bottom three. We are just concentrating on what we do.
"I know it is a cliche, but we have got another game on Saturday.
"We have got to do it now. Saturday is a massive game for us at home.
"Our main focus is staying in this league. We have got a cup game but for myself and everyone, we are concentrating on beating Hull.
"Obviously it would be nice to get a run in the cup, but we could do without the replay and our main priority is staying in this league."
Johnson insists belief in the dressing room has not wavered, but they must start converting that into performances.
He said: "We go into every game hoping we can win and we are confident.
"We have had a chat about this game and people have said their bit.
"Now we have got to stop talking off the pitch and do it on the pitch."