Croatia's Milan Badelj celebrates scoring their first goal.
Moments later Ingason, who plays his club football for Rostov, went even closer but his header hit the crossbar.
As underdogs, Iceland - along with fans and their emblematic "thunderclap" celebration - drew worldwide admiration on their thrilling run to the quarterfinals at the European Championships two years ago, holding winners Portugal in the group stage and knocking England out at the last 16.
Both the teams were 1-1 till the end of the game before which Ivan Perisic shattered Iceland's dreams with a commendable strike to drive the ball into nets awarding his team 2-1 win in the game.
Iceland were unable to react against the growing threat Croatia were proving.
They began their campaign brightly with a 1-1 draw against Lionel Messi's Argentina but that would be their only point as they finished bottom of Group D.
A Nigeria draw or loss opens the door for Iceland, which must win and win any potential tiebreaker with Nigeria (in the event of a draw in the other Group D match) or Argentina (in the event of a win over Nigeria).
Croatia have won three consecutive World Cup matches for the first time.
But Iceland's fighting spirit ultimately proved for nothing, Perisic securing a third successive win for Croatia, who will be joined in the last 16 by Argentina following their dramatic win over Nigeria.
The Icelanders were denied the lead in spectacular fashion in first-half stoppage time.
There would be a final chance before the referee called things off for the halftime break, with Aron Gunnarsson curling what would have been a worldie towards goal from just inside the box in the second minute of stoppage time. I don't know how we would go into a game not wanting to win and not wanting to play well.