In the UEFA Nations League match at Stade de France on Friday, Zidane's team was denied the win largely on the back of a fine performance from Italy's goalkeeper Gianluigi Donnarumma.
Michael Olise put France ahead in the 55th minute with a curling shot from 20 metres which went in off the crossbar, following a short free kick taken by Rayan Cherki.
Poor defending midway through the second half allowed central defender Alessandro Bastoni to run through and clip a low shot inside the right post to secure Italy the 1-1 draw.
"I'm disappointed for the players because we deserved better," Zidane said.
"We had chances to kill the game off but we didn't and football's like that sometimes. But it was encouraging. Honestly, I'm proud of how we played."
When Zidane's name was read out after the teams were announced, a roar filled the stadium.
Fans then broke out into chants of "Zizou, Zizou" — his affectionate nickname — and one banner read "Bienvenue Chez Toi" (Welcome Home).
Zidane's appointment as national team coach has been met with a wave of enthusiasm.
The 54-year-old took charge after the World Cup, replacing Didier Deschamps. He won his first two games 1-0, away to Turkey and Belgium in the Nations League.
Zidane was facing Italy for the first time since his infamous headbutt in the final of the 2006 World Cup, which saw him sent off in extra time in the last game of his stellar career.
For returning Italy coach Roberto Mancini there are signs of improvement.
His new tenure began with a 2-0 home loss to Belgium, followed by a 4-1 win at Turkey and now a solid performance against a World Cup semi-finalist.
In other matches on Friday, Poland thumped Romania 6-0, Belgium disposed of Turkey 3-0, Hungary beat Georgia 1-0 while Bosnia and Herzegovina and Sweden played out a 1-1 draw as did the Faroe Islands and Slovakia.
For Belgium, former Manchester City playmaker Kevin De Bruyne opened the scoring after nine minutes with a fine low finish before the 35-year-old added an explosive second in the 59th minute when he curled into the top corner from range.
Romelu Lukaku rounded off the scoring with 14 minutes left to move Belgium up to second and one point behind leaders France in Group One.
In Poland's Group Four win, Robert Lewandowski hit a hat-trick after Radu Dragusin, on loan at Fiorentina from Tottenham, was sent off in the 22nd minute for Romania.
While in the Group Two of the B League, Northern Ireland recorded an impressive 3-0 win in an away tie with Ukraine thanks to Ciaron Brown's brace.
Isaac Price was also on target for Michael O'Neill's young side.
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