However, the Croatia captain returned to bravely take one of the post-match kicks as goalkeeper Danijel Subasic saved three of Denmark's efforts to set up a quarter-final meeting with hosts Russian Federation, who also won in a penalty shootout earlier on Sunday against Spain after a 1-1 draw.
Free-kick to Croatia after Rebic goes down in a challenge.
It didn't take long for the Croats to equalise, though, as Mario Mandžukić drew his side level nearly immediately after the restart to net from close range and against the run of play, 1-1.
Danish star Christian Eriksen believes his team can defeat Croatia within the regulation 90 minutes.
39' - A set piece for Croatia nearly results in a goal. This could be risky. He curls the ball into the box to find Lovren but he heads it wide. Christian Eriksen crosses it in the middle but the goalkeeper makes a comfortable save.
Rebic, along with Andrej Kramaric and Ivan Perisic may feature ahead of the midfield duo of Modric and Rakitic. Denmark run down the other end, before Eriksen wins a corner. Jorgensen brought him down from behind, and a yellow card was given as per the recent rule where you can't have a penalty kick and a red card if the player is going for the ball.
In a tournament packed with excitement this was no classic, although it looked set to be a thriller after Mathias Jorgensen and Mario Mandzukic scored at either end within the first four minutes.
Rakitic sends Croatia to the Quarterfinals! His 31st goal for Croatia. A long throw-in fell for Mathias Jorgensen by the far post, and he squeezed his left-footed chance through traffic for the first worldwide goal of his career to cement a dream start for the Danes. Denmark take the lead.
Croatia celebrate their round of 16 Fifa World Cup win over Denmark.
But Croatia won the shootout 3-2 after Danijel Subasic saved three spot-kicks.
Again, the goal owed more than a little to bad defending when a Sime Vrsaljko cross was hammered by Henrik Dalsgaard into fellow Dane Andreas Christensen and the ball fell obligingly in the penalty area to Mario Mandzukic who scored.
Croatia entered the match after impressing in the group stage, including a 3-0 dismantling of two-time champion Argentina at the same stadium.
They are in fine form, too, riding an 18-game unbeaten wave.