Despite defeat, Morocco also leave with heads aloft after becoming the first African side to reach a World Cup semi-final.
Mislav Orsic's late first-half strike was enough to settle the contest after two early goals inside the first nine minutes set the tone for a pulsating encounter, Achraf Dari cancelling out Josko Gvardiol's opener for Croatia.
There were signs of nerves from Morocco early on with goalkeeper Yassine Bounou nearly scything a clearance into his own goal in just the third minute.
Croatia started the game on the front foot and took the lead in the seventh minute through a cleverly worked set-piece.
A cross floated into the box found Ivan Perisic who expertly headed the ball into the mix where the masked Gvardiol bravely dived in for the header to silence the Moroccan contingent, albeit briefly.
Two minutes later, Morocco responded at the other end with a set piece of their own when a cross came off Lovro Majer's head and looped into the box where an unmarked Dari beat the keeper with a header.
Emboldened by the equaliser, Morocco began to find chinks in the Croatian defence, with their movement and slick passing helping to create several chances.
But the African side lacked the killer instinct in front of goal, the final pass or touch always found wanting.
Croatia duly punished them in the 42nd minute when an interception in the final third found Orsic, whose curling shot arced beautifully from a tight angle past the outstretched arm of Yassine Bounou before going in off the post.
The second half did not start as fast or feisty as the first as exhaustion after a long tournament finally seemed to have caught up with both teams, playing their seventh game in Qatar.
Mateo Kovacic could have put the game to bed for Croatia in the 87th minute when through on goal but shot wide while Youssef En-Nesyri came close when he headed over in stoppage time.
But despite Morocco's best efforts to find an equaliser, Croatia held on for victory and the bronze, matching the feat of their heroes from 1998 who also finished third.
Morocco broke new ground for Africa by reaching the final four. As Regragui promised, they still go home to a hero's welcome.
