The 26-year-old was named captain after the retirement of club legend Javier Zanetti at the end of last season and Ranocchia's first league game as skipper ended in a 0-0 draw at Torino.
Inter were perhaps fortunate not to lose that encounter, with the hosts' Marcelo Larrondo missing a first-half penalty, while Nemanja Vidic's Serie A debut was far from ideal.
The former Manchester United man was sent off in stoppage time in Turin and will miss Sunday's clash against Sassuolo at San Siro.
Without a trophy since their Coppa Italia win in 2011, Ranocchia believes it is time for Inter to challenge for silverware once again, starting against Eusebio Di Francesco's charges.
"They're a good side and we must keep our guard up," he told Sportmediaset.
"I'm excited - I really want to show what I can do. I want to put this club back where it belongs.
"The boss [Walter Mazzarri] is really fired up this season. We've got a group of new players who want to embark on a journey which will lead to the team winning an important trophy."
Like their hosts, Sassuolo earned a point from their league opener after a 1-1 draw with Cagliari.
Simone Zaza's nine league goals helped Sassuolo retain their top-flight status last season and the 23-year-old opened his account for this campaign against Cagliari with a stunning left-footed volley.
Zaza's performances earned him a call up to the Italy squad for the recent games against Netherlands and Norway, and the striker netted his maiden international goal in the 2-0 Euro 2016 qualifier victory in Oslo.
The man himself has shrugged off comparisons with Mario Balotelli, while Sassuolo president Giorgio Squinzi has warned Juventus that they will have to spend big to bring back their former player.
Sassuolo signed Zaza outright from Juve in June this year and the in-form striker will be confident of causing Ranocchia and the rest of the Inter defence problems on Sunday.
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