The Icelandic midfielder marked his full debut with a half-volley from well beyond 40 yards out that sailed majestically over Hajduk goalkeeper Dante Stipica and levelled the scores at 1-1 on the night.
His strike out of the blue, just seconds into the second half, cancelled out Josip Radošević's own stunner two minutes before the break and effectively put this playoff tie beyond the Croatians who also saw Ahmed Said's penalty saved by Jordan Pickford.
"I saw Gylfi's goal, but I don't think everyone on the bench did," Koeman said. "It was incredible. I don't have any other word for it.
"You need to be really clever to see that possibility and, after two or three weeks of the season, it could be the goal of the season."
The Dutchman also had plenty of praise for Pickford who nipped in the bud any rally by Hajduk in the second half when he guessed right and pushed Said's spot kick away to safety for Michael Keane to hack clear.
"The penalty save was key as well because there were still 30 minutes to go at that time," Koeman continued. "Jordan is showing that we made the right decision to sign him.
"He is still a young goalkeeper and I have been really impressed by what he's done from day one here.
"It is an important position in the team. There's a big future for Everton and a big future for him."
Koeman confirmed that midfielder Idrissa Gueye had been left out of the travelling squad as a precaution after he felt his hamstring slightly following Monday's draw with Manchester City.
With another important away day at Stamford Bridge to face Chelsea on Sunday and Morgan Schneiderlin ruled out through suspension, the club's medical staff were taking no chances with the Senegalese midfielder.
"It was too risky to start [Idrissa]," the manager explained. "He had a scan on his hamstring and everything was fine, but we didn't want to take the risk with Morgan Schneiderlin out of the game on Sunday."