Goals from Mario Mandzukic and Darijo Srna guided Kovac's men to victory in Zagreb, with the Bayern Munich striker sent off for a reckless challenge late in the first half.
Despite playing with 10 men, Kovac felt his side dominated at the Stadion Maksimir and could have sealed an even bigger win. Iceland had a player sent off in the first leg, which finished 0-0, and Croatia was criticized for failing to capitalize.
"It's not easy to play against a team with a man down. You were a bit critical of the way we played over there with a man extra. It's tricky," Kovac told reporters. "Morality is very important, we have to be together. Today we were excellent in attack and defense. We could've scored four or five goals."
Luka Modric, who was criticized for his performance in the first leg, was a standout in the second leg, but Kovac praised his entire team.
"I want Croatia to play like this against everyone," the coach said. "Everyone gave their all and before that they were fighting. This is just the beginning of what I want."
Kovac had no complaints about the red card shown to Mandzukic for his sloppy studs-up challenge on Johann Gudmundsson in the 38th minute. Mandzukic was sorry for his tackle, and Kovac said he could see at halftime his players would go on with the job.
"It was very fast – a deserved red card. It was a heavy enough challenge," Kovac said. "When I saw the passion in my players' eyes at halftime, I knew we would push to the end. Tonight was a demonstration. Congratulations to my players."
Iceland coach Lars Lagerback lamented his team's poor efforts with possession after it struggled to create chances.
"We didn't use the ball well enough," he said. "It is disappointing to lose. We needed to take advantage of the red card. We need to learn from this game."
Iceland striker Eidur Gudjohnsen, 35, said it was likely to be his last game for the national team.
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