The Martinez era is under way at Goodison Park, and for the first time in 12 years David Moyes is not overseeing preparations for the new campaign.
Everton's friendly fixtures began with defeat to Austria Vienna on Sunday.
And in the aftermath of the game, captain Jagielka told the club website: "It's been drastically different to what we've done before but it's been enjoyable.
"It's been a lot more training with the balls and a lot more concentration required - and that sometimes isn't the easiest thing when you're tired. It's been tough but pre-season is always tough.
"Sunday's result wasn't exactly what we wanted but we can still look at a few positives and this can put us in good stead for the next few weeks."
Matthew Kennedy, Francisco Junior and Conor McAleny were among the young players used against Vienna in the absence of several senior players.
Jagielka said: "In terms of their attitudes and their ability, they've all done really well.
"It's nice for the manager to give them all game time. He could have just brought them all on for 10 minutes at the end but it was nice that most of them got 45 minutes.
"It's a test now to see if they can stay in the squad when a few more senior members come back."