Juventus were frustrated by an inspired performance from FC Copenhagen goalkeeper Johan Wiland as they were held to a 1-1 draw in their Champions League opener in Denmark.
The visitors missed a succession of chances, especially after the break, as they began their Group B campaign slowly.
At half-time, it looked as though things could have ended up worse, with the Danes leading through Nicolai Jorgensen's 13th-minute goal, but Fabio Quagliarella levelled nine minutes into the second half.
Quagliarella also headed against the bar as the Italians created enough chances to win several games, only to see them go begging thanks to a series of splendid saves by Wiland.
Conte had warned his side ahead of the match that they could not afford the sort of slow start to the competition they had last year, when they drew their opening three games before recovering to qualify.
But his team appeared not to heed his advice.
Carlos Tevez fired wide following an Andrea Pirlo corner as they served an early warning to the hosts, but the Italians fell behind when Pierre Bengtsson swept a free-kick into the area and Jorgensen was on hand to slot the ball home from close range.
Juventus almost responded in the 20th minute, but Wiland produced two superb saves to keep his side in front.
First he tipped Giorgio Chiellini's header from an Arturo Vidal cross over the bar and then, from the resulting Pirlo corner, turned away Paul Pogba's effort.
The Italians kept coming, Angelo Ogbonna heading over and Quagliarella and Tevez shooting over.
Pogba then had another golden chance, only to head wide as the visitors trailed at the break.
Conte's side started the second half in similar vein, Tevez bringing another save from Wiland.
But the 32-year-old keeper was finally beaten in the 54th minute when Federico Peluso fed Quagliarella, who fired high into the net from the centre of the area.
The search was now on for the winner, but still Wiland proved a huge obstacle.
He parried Pirlo's driven shot from just outside the area and then made a rather easier stop to keep out Stephan Lichtsteiner's effort two minutes later.
When Quagliarella beat him again in the 64th minute, the crossbar came to the keeper's rescue as the striker's header stayed out.
Vidal was the next to be denied by Wiland before the wasteful Pogba headed wide from a Pirlo cross.
Still Juventus carved out chance after chance, and produced miss after miss.
Sebastian Giovinco's shot from the right side of the area was blocked by Wiland, who saw Tevez's injury-time effort go harmlessly wide as Copenhagen held out.