Joan Carrillo's side finished third in the Croatian league last term and defeated Danish club Brondby, 2-0 on aggregate, in the third qualifying round.
Koeman will certainly not recall also fondly on the general efficiency of his side, but he will be happy to have come through a potentially hard connection ahead of Friday's pull in Switzerland.
The Toffees will find out today who they will meet in the final play-off round later this month before the group stages begin.
Big-money summer signing Jordan Pickford started in goal for Everton and kept a clean sheet, though came under precious little pressure.
US Not Seeking to Topple North Korea Regime, Says Tillerson
On Tuesday, Mr Tillerson appeared to try to clarify the U.S. stance, saying: "We have been very clear with the Chinese". United States officials have steadily condemned North Korea's missile tests, which are a violation of worldwide law.
Calvert-Lewin's smart finish sealed Everton's progress though, leaving Koeman satisfied with the night's work.
"Maybe Dominic [Calvert-Lewin] feels a bit more comfortable out of the system we played tonight, where he is one of two strikers", Koeman said.
"But we know we can, and we need, to improve in our ball possession".
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