|11/2||Juve are 11/2 with Coral to win Group B
The visitors took a surprise lead through Didier Drogba, before a 78th-minute penalty from Arturo Vidal saw the Bianconeri draw level.
Umut Bulut salvaged a point for Gala in the closing stages following Fabio Quagliarella's strike moments earlier but Mancini - who was taking charge of the Turkish giants for the first time - believes Conte's men owe their point to the referee.
"It was a strange game, as Juve went behind and they were awarded a penalty which was, shall we say, strange?" he told Sky Sport Italia.
"I don't think they would have been able to score tonight without the penalty and I don't think [it] should have been one."
The former Manchester City trainer went on to pay tribute to Didier Drogba, 35, who produced a performance which exceeded his own expectations of the Ivorian.
"Drogba was incredible," he added. "I did not expect him to play like this. He was extraordinary."
The result leaves the Turkish champions sitting bottom in Group B on one point, behind Copenhagen on goal difference and trailing Real Madrid and Juve by three points.