Their meetings in the recent World Cup qualifying campaign ended with Gordon Strachan's side withdrawing maximum points, while also bringing out the worst in a side which finished second in Group A but without a manager. Igor Stimac had departed the dug out at Hampden intent on offering to resign but the Croatian Football Federation beat him to it - sacking the 46-year-old yesterday.
It had not been the only item on the agenda for president Davor Suker, a celebrated member of the Croatia national team during the '90s and a former team-mate of Stimac. The sight of Steven Naismith tucking in a second goal for Scotland on Tuesday night had proven too much for Dejan Lovren and Ivan Strinic, the Croatian pair becoming embroiled in a heated exchange which is understood to have erupted again in the dressing room after the match.
Both were fined an equivalent of £17,000 and censured for "damaging the reputation of the national team", with Lovren adding a public apology yesterday. "It all happened in the heat of the battle. I told him I was sorry and it happened because I don't like to lose," said the Southampton defender.
The reaction of dismissing Stimac was not a rush of blood to the head, though. The former Derby County defender had been in the post for 15 months and, while two defeats to Scotland will seem like an affront to many of his erstwhile team's fans, a listless performance against group winners Belgium seemed indicative of a much wider malaise.
"We have to look at the reputation of the national team," said Suker. "[It] was not acceptable to lose in Scotland in such a manner and it was a unanimous decision from the board. The poor recent results and performances are not of a standard that we expect from the Croatia national team."
Finishing in a play-off spot behind the Belgians was, though, and Niko Kovac, previously in charge of the nation's under-21 side has been placed in charge on an interim basis. The former Bayern Munich player has time before potentially taking charge of a play-off match but his greater concern will be in reinflating the national team's morale.
"It wouldn't matter if we had three Jose Mourinhos in charge of us after that performance [against Scotland]," said Stipe Pletikosa, the Croatia goalkeeper. "If we don't change quickly, we won't be going to Brazil."
It was a common sentiment. "I have been with the team 11 years and that was the worst [result] . I was ashamed of that," added captain Darijo Srna.