Esteban Cambiasso was relieved with the defensive solidity shown by Inter in their 2-0 win over Genoa on Sunday.
The Nerazzurri made a winning start under new boss Walter Mazzarri and the Argentine thinks the scoreline is significant.
“It was very important to win without conceding,” the central midfielder told Inter Channel after the San Siro victory.
“It was vital because we have to make sure that goalkeeper Samir Handanovic is not always our man of the match…”
Inter conceded 57 goals last season in the League – only Pescara had a worse defensive record in the top flight.
The Beneamata netted the points at the weekend with goals from Yuto Nagatomo and Rodrigo Palacio, but it took some time for Inter to break down the Grifone.
“We needed to be patient because teams often come here to defend and you can risk being caught out on the counter,” the former Real Madrid man added.
“The team is improving, but this is just the start and there are lots of things to learn and work on. Our play wasn't as good as I think it can be and we need to improve in that area.”
Inter are away at Catania in Week 2.
Tickets for the Champions League final between Juventus and Real Madrid are still on sale with reseller Viagogo - Click to find out more