The Giallorossi have lost three of their last four league matches - a run which has seen them fall 10 points behind third-placed Lazio - but the defender insists reaching Europe's elite club competition is not out of their reach, providing they win on Sunday.
"I remember our last victory at San Siro," the former Corinthians centre-back told Sky Sport 24. "It was a good match and I expect it to be the same on Sunday.
"It will be crucial in the race to finish third and we have to win. Third place is still possible, but only if we beat Inter.
"I could've stayed at Corinthians but I wanted to play in Europe. Roma showed me their project and I said 'yes'.
"I could have stayed in Brazil until January but [sporting director Walter] Sabatini wanted to bring me to Italy immediately.
"I expect to win the Scudetto and the Coppa Italia with Roma, but a lot of work still needs to be done."
Castan also spoke highly of the club's younger players, reserving special praise for fellow stopper Alessio Romagnoli, and believes their emphasis on promoting youth could give them the edge at the Giuseppe Meazza.
"There are many good ones, especially [Alessandro] Florenzi, [Mattia] Destro and [Alessio] Romagnoli," he added.
"The latter has great potential, I try to help him because I'm sure he can become a champion one day. Totti? He is too strong."