For the briefest of moments, the Icelandic dream flickered. Gylfi Sigurdsson had shown the kind of courage that has come to be associated with his country when he stepped forward to address a 76th-minute penalty, having missed from the spot in the previous tie against Nigeria.

This time, he found the roof of the net and, when the news filtered through of Marcos Rojo’s 86th‑minute goal for Argentina that put them 2-1 up against Nigeria in the other Group D tie, the equation became tantalisingly simple.

Iceland needed one more goal. A 2-1 win would have sufficed. It would have taken the smallest nation to compete at the World Cup into the knockout rounds. They had the time to get it and the momentum was with them.

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Reality would intervene with a thud. Croatia, who had already qualified, had rested players and they performed largely within themselves, although they did rouse themselves in the second half. The tie hurtled into stoppage time, the drama crackling until the dying embers, but when Ivan Perisic fastened on to a slide-rule pass, the Croatia winger banged his shot into the far, top corner.

For Iceland, it was over.

There would be pride in defeat but also regret, with the biggest one being the failure to punish Nigeria in a game when they were on top in the first half. Iceland would lose 2-0. Heimir Hallgrímsson, the manager, talked of having played five good halves at this tournament and one bad.

The other window for a one-goal Iceland victory had come after Lionel Messi put Argentina 1-0 in front with an early goal. The permutations would lurch throughout the evening but, in the end, Iceland could not look after what they needed to do. They did not have the requisite quality in front of goal when it mattered the most.

Facebook Twitter Pinterest Gylfi Sigurdsson scores from the penalty spot to give Iceland hope of winning the game and qualifying from Group D. Photograph: Vadim Ghirda/AP

Croatia advanced into a last-16 tie against Denmark in Nizhny Novgorod on Sunday with maximum points and they could feel that the victory showcased the depth in their ranks. This squad – and every other one from their borders for the past couple of decades – has lived in the shadow of the great 1998 team who reached the semi-finals in France. Could this be the year when a new crop finally emulates them? It is the first time since then that they have reached the knockout phase. “Denmark is our moment of truth,” the manager, Zlatko Dalic, said.

Iceland’s threat came from corners and Aron Gunnarsson long throw-ins – their physicality and directness is their greatest strength – but they also pieced together moves of promise and no little thrust. They had a flurry of chances before the interval and, when none of them went in, it was easy to fear that it would come back to haunt them.

Alfred Finnbogason robbed the dawdling Milan Badelj on 41 minutes and, after he swapped passes with Gylfi Sigurdsson, he whistled a shot wide of the post. Iceland could not catch a break. Birkir Bjarnason, who had earlier been bloodied by Marko Pjaca’s elbow, saw a shot blocked by a combination of Duje Caleta-Car and the foot of the goalkeeper Lovre Kalinic, while Gunnarsson was also thwarted by a diving Kalinic save.

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Dalic’s wholesale changes had been anticipated but the surprise inclusion in his lineup was Luka Modric. The idea was that he would control the tempo but it did not really work out like that, despite some lovely touches from him. Dalic’s only other first‑choice in the starting XI was Perisic.

Croatia offered nothing as an attacking force in the first half but they were more threatening after the break and they might have led when Badelj’s shot from distance deflected off Ragnar Sigurdsson and rattled the crossbar.

Iceland felt a couple of sucker punches in the moments that followed. First, Victor Moses equalised for Nigeria, which was not good for them, but worse was to come. The Croatian incision came from the full‑back Josip Pivaric, and it was a sharp one.

He crossed from inside the area on the left and, when it deflected, it sat up for the advancing Badelj. He still had plenty to do but the technique and timing of the finish were excellent. Hannes Halldórsson was powerless. At that point, Iceland need to score three times to overhaul Nigeria.

They continued to fight and created further chances. Sverrir Ingason saw a header tipped over the crossbar before he sent another one against the woodwork while Bjarnason sliced horribly when gloriously placed from Finnbogason’s cross.

Hallgrímsson went for broke, replacing the centre-half Ragnar Sigurdsson with the forward Björn Sigurdarson, and Sigurdsson’s penalty, awarded for handball against the substitute Dejan Lovren, represented a lifeline. Rojo’s goal brought another and the hope would surge. Perisic snuffed it out.