The Premier League leaders have been left short at the back by the Belgian's absence, with fellow centre-back Kolo Toure also missing due to African Cup of Nations duty, but the Montenegrin is confident he can step up.
"When you are replacing someone like Vinny, everyone expects a lot from you," Savic told the club’s official website.
"He is our captain and our leader. But I think I can do it.”
The 21-year-old faced a tough battle against Liverpool in Wednesday's League Cup semi-final first leg, conceding the first-half penalty that handed Kenny Dalglish's side a 1-0 advantage going into the return tie at Anfield in two weeks' time.
However, the £6 million signing from Partizan Belgrade rallied in the second half, and Savic is still confident of reaching the final at Wembley in February.
He added: "The first half was difficult and the tackle for the penalty was a bad decision from me.
"But after that we came back into the match and had some chances and we still have a chance to go to the final."