The former Biancocelesti captain made the switch to the San Siro this week after becoming frustrated with a lack of first-team opportunities.
And with a nine-point deficit to leaders Juventus, he is focused on helping his new side into second place - they are currently third, trailing Lazio by a point ahead of Sunday's clash with Udinese.
"We'll be second in front of Lazio," Rocchi predicted on Sky Italia, before revealing his unhappiness prior to the move.
"In Rome I was nothing but the deputy to (Miroslav) Klose," he said. "I was no longer considered for the team.
"I've already talked with (Inter coach Andrea) Stramaccioni about it, I will always put myself at his disposal ready for action."
Juve, weakened by the absence of defenders Giorgio Chiellini and Stephan Lichtsteiner, midfielders Kwadwo Asamoah and Simone Pepe and striker Nicklas Bendtner, take on Sampdoria on Sunday.
The defensive position, at least, could be strengthened with Atalanta's Federico Peluso expected to sign before the weekend - while the club are also looking to develop their squad in the longer term by opening talks with Athletic Bilbao striker Fernando Llorente over a summer move.
The Spain international is out of contract at the end of the season and a Bilbao statement today read: "Juventus Football Club informed Athletic Club on January 3 that, knowing Fernando Llorente will end his stint at our club on June 30, 2013, they will begin negotiations with the player to incorporate him into their squad."
High-flying Fiorentina take on Pescara while the teams occupying fifth and sixth positions, Napoli and Roma, meet in Naples.
The hosts have been linked with Siena pair Emanuele Calaio and Neto, with Siena president Massimo Mezzaroma warning them they will have to pay a hefty fee.
"Calaio to Napoli? Emanuele is a key player for us and we know it," he told ANSA.
"We must meet the needs of Siena. Of course, to deprive us of Calaio, Napoli must pay the best price."
Roma would move ahead of their opponents with a victory and defender Nicolas Burdisso has called on them to improve their consistency after a first half of the campaign which brought 10 wins but also six defeats.
"In 2013 we must achieve continuity, that's the main thing." he told ANSA.
Siena - who are also prepared to listen to offers for Marcelo Larrondo, while sporting director Stefano Antonelli confirmed to Sky Italia his interest in Inter's Croatian striker Marko Livaja - travel to AC Milan on Sunday.
Milan are also at the centre of transfer discussions, with Alexandre Pato set to join Brazilian side Corinthians for a reported 15million euros (£12.2m) - much of which could be immediately reinvested in Anderlecht's Lucas Biglia.
The midfielder has been linked with the Rossoneri and his agent Enzo Montepaone told Tuttomercatoweb: "Lucas Biglia will leave Anderlecht in this transfer window. The boy would very willingly play in Italy."
Sunday's other games see Atalanta travel to Chievo while Genoa host Bologna and Parma face Palermo.
Lazio cut Serie A leaders Juventus' lead to five points on Saturday night with a 2-1 home win over struggling Cagliari.
It took a late penalty from Alvaro Candreva to decide the outcome, with Cagliari having two men sent off after the spot-kick was awarded.
Goalkeeper Michael Agazzi was dismissed first, receiving his second yellow card of the game for the foul on Miroslav Klose that resulted in the penalty, and for protesting excessively midfielder Andrea Cossu was also ordered off.
Cagliari had gone ahead after 62 minutes when Marco Sau struck, but Abdoulay Konko levelled 10 minutes from the end and in the 86th minute Candreva secured all three points for second-placed Lazio.
Juventus still have a comfortable cushion, and on Sunday can restore their eight-point advantage when they tackle Sampdoria in Turin.
Earlier, Catania and Torino shared a tame goalless draw at the Stadio Massimino in the first Serie A game of 2013.
The Sicilians held on for a point, despite playing nearly the full game with only 10 men following an early red card for Francesco Lodi, who lashed out in retaliation towards Riccardo Meggiorini and receiving his marching orders from referee Mauro Bergonzi.
Catania squandered a penalty when Gonzalo Bergessio sent his kick against the crossbar.
Saturday's Serie A Results
Sunday's Serie A Fixtures