The Merseyside club are getting used to new manager Roberto Martinez and have won two of their three pre-season fixtures, their latest success a 3-1 win at Blackburn on Saturday, with Nikica Jelavic scoring twice to boost his chances of a first-team spot under the Spaniard.
"This is the strongest squad we've had for pre-season for a while," Jagielka told Everton's official website.
"Normally it's been interrupted and we've only had 12, 13 or 14 players but the manager has got probably 16 to 18 players plus a few of the younger lads on the periphery as well."
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"It's always nice to be scoring goals and the most important thing is to be creating chances - we did that a lot in both halves," he added. "We could have created a few more but we're not going to get carried away - it's only pre-season and a few of the boys have only been back a week or so.
"We're still building up for the start of the season and, hopefully, when you speak to me in a few more weeks we'll be converting even more chances and looking more solid at the back.
"The manager is excited with the potential he sees and that is the state of play at the moment. We're nothing like a finished project yet, but we put in a really good performance.
"We're a little bit disappointed to concede the goal but, other than that, I thought we pretty much controlled the game. We gained valuable minutes and a few of the lads came back a bit later than others so it was nice to see them get their first outing and nice for Jelavic to get a couple of goals."