Croatia crossed the Adriatic hoping to protect an impressive unbeaten record against the Italians that stretched back to 1942 when the Azzurri beat the then Yugoslavia 4-0 in Genoa.
Instead, Croatia coach Niko Kovac spent most of the post-match period making apologies for the disruptive behaviour of his country's notoriously difficult fans.
"I want to say sorry for what happened with our fans," said Kovac, a former captain of Croatia. "This is not football and it's not a fair image of our country or our people.
Kovac, a former captain of the national team, ultimately saw his side underline their superiority against an Italy side which, after a second consecutive first-round exit from the World Cup last summer, is now in construction mode.
With an impressive crowd of 66,222 fans inside a packed San Siro, Lazio midfielder Antonio Candreva got the hosts off to a great start in the 11th minute with his debut goal for the Azzurri.
But four minutes later, Croatia were back on level terms.
Three Italy players backed off while Ivan Perisic was in possession on the left flank and the Wolfsburg midfielder drilled a low shot under the body of 'keeper Gianluigi Buffon.
Croatia suffered a blow when Luka Modric hobbled off before the half-hour to be replaced by Inter Milan playmaker Mateo Kovacic.
But the visitors made light of the Real Madrid midfielder's absence for the remainder of a match that they should have wrapped up in the final 10 minutes only for Perisic, left in acres of space on the left flank, to fire a great chance wide of Buffon's far post.
Croatia remain top of Group H with Italy still in second spot having now failed to beat their rivals in their past seven games.
However the UEFA spotlight will again shine on the Baltic nation, who have been issued with sanctions in the past for fans' behaviour.
The first signs of any kind of unrest within the stadium appeared shortly after kick-off.
Several rocket flares were thrown in the early stages of the game and loud bangs echoed around the stadium after being set off in the Croatia fans' end.
Around the hour mark, the incidents reached boiling point. With most of the players camped in Croatia's end, Italy and Juventus goalkeeper Buffon became a target as fans launched flare after flare in his direction.
The match was halted momentarily, but officially postponed minutes later by referee Bjorn Kuipers as flares continued to hit the pitch.
The players returned to the pitch approximately 10 minutes later and the match resumed with Italy and Croatia both spurning chances to snatch a late lead that would have pulled either team clear of the other at the top of the group.
Croatia's fans have a reputation for troublesome behaviour at matches and flares are regularly fired at Croatian league matches.
But Kovac said such behaviour had no place in the sport.
"There are kids in the stadium. This is not football and it's not a fair image of our country or our people," he said.
Conte commented: "I hope the people who carried this out and the people who seen it have no intention of doing it again."
The Azzurri coach's biggest worry, however, is Italy's apparent inferiority to a Croatia side whose biggest achievement in international terms was a third-place finish at the 1998 World Cup, a competition Italy have won four times.
"Croatia are strong, they're well-prepared and have great individual players who play at the top level. They gave us a tough match," said Conte.
However, he added: "In the circumstances and in terms of our objectives, I'm happy with our performance.
"I don't want the media to criticise our squad. We still have progress to make."