Inter now face little Trapanda in the next round.
"Aside from the result, the important thing was to put in a convincing performance," Mazzarri told SportItalia.
"We were a little anxious at first and some players felt the nerves of the season debut, but then we relaxed and the team was convincing at times.
"Cittadella were in better shape compared to us, as they had played the previous round, but we must not consider the result. We just have to focus on improving.
"Ricky Alvarez is doing well, but needs to be more consistent from game to game. He has great quality.
"My first official match on the Inter bench gave me a great sensation, but it was embarrassing when I was heading for the wrong bench. It wouldn't have been so bad if I hadn't asked Diego Milito beforehand which one it was "
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