Both of our players competed the full 90 minutes as their side suffered a late 1-0 defeat against reigning champions Spain.
Jesus Navas scored two minutes from time to see Spain to the top of Group C and through to the quarter-finals. Italy's 2-0 win against the Republic of Ireland secured second spot for the Azzurri and relegated Croatia to third.
Having contained Spain for the first half, Croatia started to push further forward in the second half and Luka was instrumental in creating the best chance of the match on the hour.
He broke away from Sergio Ramos on halfway and sprinted down the right, cut inside Alvaro Arbeloa and delivered a pinpoint cross with the outside of his right foot to Ivan Rakitic, unmarked at the far post.
Rakitic dived in to meet the header eight yards out but couldn't angle it away from Spain goalkeeper Iker Casillas, who palmed away.
As Croatia continued to press, Vedran looked to have his shirt pulled going for a corner that he headed over, but nothing was awarded.
Spain finally broke the deadlock and Croatia hearts when Cesc Fabregas found Andreas Iniesta in the box and he squared for Navas to tap into an empty net.
Attention now turns to England and the completion of the group stages on Tuesday night.
Scott Parker and Jermain Defoe are with the Three Lions who will look to finish top of Group D - and therefore take on Italy, not Spain in the quarter-finals - by beating Ukraine at the Donbass Arena and hopefully top France's score against Sweden.
Both matches kick-off at 7.45pm UK time.