The Montenegro international striker had been set to join Walter Mazzarri's side, with Fredy Guarin heading to the Juventus Stadium in an exchange deal.
However, Inter owner Erick Thohir pulled out of talks on Tuesday claiming the transfer did not meet "technical and financial conditions".
Barzagli revealed the squad had said their farewells to Vucinic, but says the team will have no issue with the 30-year-old.
"He had emptied his locker," Barzagli said. "We said goodbye to Mirko and he was an integral part of two and a half fantastic years.
"If he returns we'll embrace him again."
Barzagli was speaking after seeing Juventus exit the Coppa Italia at the quarter-final stage in a 1-0 defeat to Roma thanks to Gervinho's 79th-minute winner.
And the Italy international conceded the team failed to make the most of their opportunities.
"We're disappointed to go out of the Coppa Italia, as this was one of our objectives," he added.
"What did we get wrong? The goal. We knew it would be a balanced encounter that would be decided on incidents.
"We had a few chances, but the goal came late and we didn't have time to turn it around."
