A match that had to be halted for a few minutes in the first half when trouble flared in the away section at Goodison Park saw the hosts go in at the interval two goals up thanks to a Michael Keane header and an Idrissa Gueye strike.
Everton were not so dominant in the second half and goalkeeper Jordan Pickford was called upon to make several decent saves to ensure Hajduk did not nick a goal ahead of next Thursday's second leg in Croatia.
Asked how he felt about his team's efforts after the contest, Koeman said: "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.
"This is two legs, and with a better result it would be even more easy. It will be difficult now."
Asked if he thought there was an attitude problem, Koeman said: "I don't know, I will ask the players. But it's not how I like to play."
The Dutchman did single out Pickford for praise, saying: "Maybe there was one on the pitch who played 90 minutes at a high level, and that was Jordan."