Everton maintained their top four aspirations with a comfortable 2-0 win over out-of-form Norwich at Goodison Park on Saturday.
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."
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