The Toffees will compete in the Europa League third qualifying round after finishing seventh last season, with Koeman having since completed big-money moves for Netherlands international Davy Klaassen and Sunderland goalkeeper Jordan Pickford.
They both signed five-year deals at Goodison Park and, at 24 and 23 respectively, Jagielka believes the future looks bright and is looking forward to welcoming further arrivals.
“It’s nice to get some business done. Obviously we know we’re going to be in Europe so we need a slightly bigger squad,” the long-serving defender told Sky Sports, with the club having also signed Dutch teenager Nathangelo Markelo to join up with the Under-23s.
“I’m sure there’ll be plenty more ins and outs before the transfer window shuts, but it’s nice to see that we’ve managed to get a few players in. Quite a few young lads as well, for the club moving forward, which is fantastic.
“I’m sure I won’t see them for a few weeks, most of them are still playing in the Under-21 [European Championship] tournament. It’s nice to see the club are progressing well.”
Having comfortably surpassed their points tally of the previous two seasons in the 2016-17 campaign, expectations are set to rise at Everton and Jagielka knows it.
He added: “You feel that. Everyone’s got that little bit more money to spend, everyone can get their squad a little bit stronger and after a pretty solid start under Ronald Koeman last year the fans will be hoping that’s we can kick on.
“That’s something we want to do. It’ll be a little bit tougher with the extra games, but it’s something that all the players are looking forward to doing.”
Pickford moved from relegated Sunderland for an up-front fee of £25million, while Klaassen was lured from Ajax for an initial £23.7m.