The Toffees won the race to land Lukaku from Chelsea on transfer deadline day, and the Belgian has been in brilliant form since his arrival with three goals to his name.
Everton remain the only unbeaten side in the Premier League and Jagielka believes that keeping Lukaku fit could be crucial.
"He's a fantastic acquisition for us," said Jagielka after Lukaku scored twice in Monday's 3-2 win over Newcastle.
"He's a great player and has probably taken us up to that next level.
"If he can keep himself fit and keep himself confident, he could be great for us.
"He has all the attributes and he loves playing football, and if you put it all together, then it can lead to some interesting days on the training pitch for us defenders.
"He's a real presence up front. Obviously he wasn't quite getting the nod at Chelsea and that's made him even hungrier than he was last season [when the Londoners loaned him to West Brom].
"He's definitely a handful, I try to stay away from him in training, to be honest!"