The visitors, under Kovac's charge for the first time, had a one-man advantage for the final 40 minutes in Reykjavik but could not find a way past the hosts' resolute defence, despite Olafur Skulason's dismissal for a foul on Ivan Perisic.
Goalkeeper Hannes Halldorsson was in excellent form to keep the home side in the tie ahead of the second leg in Zagreb next Tuesday.
But Kovac will approach the match in confident mood.
"This is not a bad result," he said. "We have the second leg at home in front of our people and we hope for good results in to get to the World Cup.
"Iceland has shown that there is a real character, endured as our pressure in the second half. We had a lot of chances, but we did not manage to achieve a goal.
"After this game, I think our team has more quality and strength. We know how Iceland play and I am sure that we will control the game in Zagreb.
"We expect that Iceland has spent more energy today than they would have liked and it could benefit us in the second leg."
