The Toffees are in the competition this season by virtue of their seventh-place finish in the league last term, and have been drawn in a group against Lyon, Atalanta and Apollon Limassol.
Last year Manchester United won the competition and secured a place in the Champions League group stages as a result, while Liverpool were runners-up the year before, and Jagielka believes that demonstrates how clubs are now starting to take it seriously.
"After seeing how United did, and Liverpool also got to the final the year before, I think it's a competition that we can target," Jagielka told ESPN. "It's a competition that a lot of people look at it and aren't sure whether to take it seriously or what sort of squad to put out in it.
"But United made a conscious effort, after not having the best of starts in the league, to put out the best team that they possibly could. They ended up winning a trophy they had never won before and getting Champions League qualification through doing so.
"We can't choose to be picky about what kind of tournaments or trophies we want to try to win. I think the manager is desperate to win something, as are the players, and the Europa League presents as good an opportunity as the domestic cups.
"I've been here for 10 years and it's the same every year. I've been to a final and a couple of semi-finals, but you want to go that bit further and win some silverware. The Europa League would be a fantastic competition to win and by doing so, it would also take us into the Champions League."
The Toffees begin their Europa League campaign away at Atalanta tomorrow evening.