The veteran full-back was pleased with his side's display and feels they must use the performance as a springboard for the rest of the season
The Nerazzurri forced the tie into extra time at San Siro after levelling the aggregate scores at 3-3, following strikes from the inspired Antonio Cassano, Rodrigo Palacio and an own goal from William Gallas.
But Emmanuel Adebayor's away goal was enough to send the visitors through, even after Ricky Alvarez's late header, and Zanetti was thrilled with the performance of his team-mates.
"We had a great game, but unfortunately it was not enough. We left ourselves out on the pitch," he told reporters.
"This was the real Inter which we must use as a point of reference [for the rest of the season]. This year there have been some negative spells, but this evening we saw lots of positive things. Cassano? Antonio, when fit, can decide matches like he did so tonight. He is a champion.
"Over the next few days, we will try to recharge our batteries for another important game [against Sampdoria] at the Marassi. We need to rediscover our consistency, and we hope to do well on Sunday."
Prior to the match, defender Christian Chivu caused something of a stir when he warned Inter that they must stop looking back on their achievements of recent years if they are to move forward, and Zanetti feels his team-mate was correct in his appraisal of the current side.
"Chivu's words? We talked about it with serenity. His was constructive criticism and he is a man of great experience. We are trying to grow for the future. He was referring only to our present difficulties, but we saw good things tonight," he added.
"We must try to find consistency from tonight's performance. We will spend time on the training ground and work hard to right our wrongs."