Simunic missed the 2014 World Cup after receiving a 10-match ban for shouting a pro-Nazi chant at the end of the 2-0 playoff win over Iceland in Zagreb in November 2013, a victory that sent the Balkan nation into the finals.
"(He) personifies decency and honesty in football," said Cacic of the former defender. "He is popular among the players and a section of the fans.
"As such he will be an important link in creating a good atmosphere and achieving positive results. I look at him as an outstanding player, a man and a patriot," he told a news conference.
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Simunic took the microphone at the Maksimir stadium, turned to the terraces and shouted 'Za Dom' (for the homeland) and the fans responded 'Spremni' (ready).
The call-and-response salute is widely associated with Croatia's Nazi-allied Ustasha regime that ruled from 1941-45 and brutally persecuted Jews, Serbs, Gypsies and anti-fascist Croats.
Simunic, 37, retired as a player in December while with champions Dinamo Zagreb.
The 61-year-old Cacic took over with Croatia's hopes of qualifying automatically for Euro 2016 in the balance after a 0-0 draw at Azerbaijan and a 2-0 defeat in Norway.
Croatia had a point deducted by European soccer's governing body UEFA after fans used a chemical agent to print a swastika on the pitch at Split's Poljud stadium before a 1-1 home draw with Italy in June.
The swastika became visible during the match, played behind closed doors after supporters shouted the 'Za Dom Spremni' chant during a 5-1 win over Norway in Zagreb in March.
The Croatians had been fined 100,000 euros ($111,420) and ordered to play their next two home games in UEFA competition behind closed doors.
They are third in Group H with 14 points from eight games, four behind leaders Italy and two adrift of second-placed Norway.
Croatia host Bulgaria on Oct. 10 and visit Malta three days later in their final two qualifiers.
The top two go through automatically to next year's finals in France while eight third-placed teams face two-legged playoffs for four remaining berths.
($1 = 0.8975 euros)
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