Sunday night's 2-0 victory away to Sampdoria meant Inter moved temporarily into second place, two points behind League leaders Milan.
"We had the same attitude with Benitez," Zanetti said. "But there were 11 or 12 bad injuries, which complicated everything.
"As long as we were at full strength, we did well. Then we lost ground.
"Leo has brought enthusiasm back to us. But we know that everything depends on us.
"If we believes in ourselves we can realise all our objectives, even if it will be tough against Napoli and Milan."