Goals from Michael Keane and Idrissa Gueye have given the Toffees a 2-0 lead in the tie ahead of next week's second leg in Croatia with both teams looking to qualify for the group stages of the competition.
However, Koeman has criticised the manner of the win, after Jordan Pickford was forced into a number of saves to prevent the visitors from getting onto the scoresheet.
The 54-year-old told reporters: "Really happy about the first half and really unhappy about the second. I think we lost a big opportunity to score more goals today and decide qualification.
"We were 2-0 up before half time, and there was a chance for Wayne [Rooney] to score the third, and then the way how we dropped the tempo in the second half. I don't think it's about we were tired after 45 minutes. I don't think our opponent made it more difficult.
"It was us, by ourselves. We dropped the tempo. Hajduk had some good chances to make it 2-1 and we were lucky. It is about the tempo of the game and trying to get the maximum out of this game. It is about intensity and the way we need to play, and the second half wasn't good."
Everton will now prepare for a Premier League fixture at Manchester City on Monday, August 21, before making the long trip to Croatia for a match which takes place three days later.