Mancini and Ranieri will meet again next week
The Italian champions conceded two late goals from Alessandro Del Piero and Jean-Alain Boumsong to lose a 2-0 lead, following Julio Cruz's brace.
Despite the tough task awaiting the Nerazzurri in Turin when the two teams re-clash for the second leg game next week, Mancio believes Inter's chances of going through are still there.
"It’s upsetting to concede two goals like that, but we played well," Mancini said after the game.
"With a numerical disadvantage we went ahead twice and I think that should give us belief for the return leg.
"I think that qualification is within our grasp as long as we go to Turin with the same spirit that we showed this evening."
Strange Game
On the other hand, Juve boss Claudio Ranieri described the game as 'strange', after Inter were down to ten men within eight minutes from the start, following Nicolas Burdisso's sending off.
"It was a very strange game," said Ranieri.
"We wanted to get a positive result and did start off well. With the extra man we tried to spread them and although we had most of the possession, it was sterile, as we never really tested Francesco Toldo."
"This team is always present and the two late goals were very important. It was crucial to score away from home in this competition to make the second leg easier."
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