The Liverpool defender came on in the 69 minute with his country leading 1-0 in Rostov thanks to a strike from Milan Badelj.
Soon after the break the match turned when Fiorentina midfielder Badelj first clipped the bar with a long-range drive, then made no mistake soon after on 53 minutes.
Buoyed by the cacophonic "Viking Thunder Clap" from the crowd, Iceland poured forward in search of the goal which would see them through into the knockout stages but it was Croatia who would laugh last, as Ivan Perisic stole in to break Icelandic hearts as the game moved into stoppage time.
Argentina took second place and will face France after a 2-1 win against Nigeria.
"We have not played many games like this against a strong team like Croatia and created as many chances as we did", Hallgrimsson told reporters.
With Five minuets remaining in the half, Iceland had another go at Kalinic's goal as Alfred Finnbogason's effort from distance sailed inches wide of the upright.
Fielding a side filled with reserves after already being assured of a spot in the round of 16, Croatia started to take control of the match in the second half.
"We've played Croatia four times in four years, we've often said we're like a married couple - we're trying to get divorced, but we always meet up again", the Iceland coach said at a recent media conference.
Argentina supporters in Buenos Aires react to Marcos Rojo's game-winner late in the second half against Nigeria. As for Croatia, it has a round of 16 date against Denmark on Sunday.
Moments later Ingason, who plays for Rostov, went even closer but his header hit the crossbar.
Though they appeared deflated in the ensuing minutes, Sigurdsson was rewarded in the 75th minute with referee Antonio Mateu awarding Iceland a penalty for a handball on substitute Dejan Lovren. But Ivan Perisic punished a defensive error to make it 2-1 at 90 minutes.
Croatia kept its flawless record at the 2018 FIFA World Cup while sending Iceland home on Tuesday.
"We did not look the best on the pitch today, but it's important to win on such occasions", said Perisic.