The Scots, playing in their first major tournament since the 1998 France World Cup, needed a victory in their final Group D fixture to reach the last 16 but despite a big effort fell short again.
Attacker Nikola Vlasic drove in the opener for Croatia in the 17th minute before Callum McGregor gave Steve Clarke’s side encouragement with a leveller three minutes from the break, his first international goal.
However, just after the hour mark, captain Luka Modric restored Croatia’s lead with a stunning strike from 20 yards before Ivan Perisic headed in a third in the 77th minute to seal the win and take the Croats through, with Scotland finishing bottom of the section with just one point.
The Scots had not lost to Croatia in their previous five meetings and were hoping to make their own football history.
Clarke made one enforced change to his side, midfielder Stuart Armstrong in for 20-year-old Billy Gilmour who was ruled out after testing positive for Covid-19 following his first start against England at Wembley on Friday night.
The Scots roared into the game, winning their first corner within 10 seconds and their second on the back of it, trying not to let their opponents settle.
Adams drove wide from long distance and it was all looking positive for the Scots until they fell behind.
Perisic climbed high above right-back Stephen O’Donnell at the back post to head a deep cross from Juranovic down to Vlasic and he took a touch 10 yards out before firing past defender Scott McTominay and keeper David Marshall, stunning the Tartan Army.
Croatia were dominating the ball and dictating the play but with three minutes of the first half remaining they found themselves pegged back.
Captain Andy Robertson’s cross was only half-cleared to the edge of the box by Domagoj Vida and McGregor took a touch and stepped on to it.
The national stadium held its breath for a moment before the Celtic midfielder drilled it low past the despairing Livakovic.
Croatia were first to threaten after the break and Marshall had to be quick out of his goal to foil defender Josko Gvardiol, who burst through the middle of the Scots rearguard.
Moments later, the Scotland keeper made another save from Perisic, who was then flagged offside, before McGinn failed to get a proper connection on an Armstrong cross just a yard from goal.
However, in the 62nd minute Scotland were back to square one and staring at the exit door.
As slick-moving Croatia penned the dark blue jerseys into their own box, Mateo Kovacic set up mercurial midfielder Modric who curled the ball sumptuously from 20 yards with the outside of his right foot past Marshall who had no chance.
Ryan Fraser replaced Armstrong in the 69th minute but there was more woe to follow when Perisic rose above Kieran Tierney to head Modric’s corner in off the far post and it was effectively over for the Scots and their fans, who will return to their armchairs to watch the rest of the tournament.