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.
Vlasic, Josip Juranovic, Bruno Petkovic and Marcelo Brozovic returned for Croatia.
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.
In the sixth minute attacker Che Adams just missed an in-swinging John McGinn cross by inches with Croatia keeper Dominic Livakovic punching clear for another corner which was repelled.