Whoever comes through that two-legged tie will meet the winners of the all-Championship semi-final being contested by Cardiff City and Crystal Palace in the final at Wembley on February 26.
City ended a 35-year wait for a trophy when they won the FA Cup last season and, although they fell at the first hurdle when Manchester United beat them 3-2 at the Etihad Stadium, they still remain in the hunt for three trophies.
Despite losing to United, Mancini was upbeat following City's strong second half fightback, when, with 10 men, they reduced the half-time deficit of 3-0 to 3-2 by full-time.
"The players showed character and have taken a step forward. I think more than ever that we can go on and win the league," he said.
"If we show the same attitude and strength in other games that we showed against United with only 10 men then, yes, we can win the league. I said we had to improve and I think we are doing so."
Liverpool, who have won the League Cup a record seven times, will also be taking Wednesday's match seriously with Kenny Dalglish expected to take a strong side to Manchester as they seek their first honour since lifting the FA Cup in 2006.
Dalglish became Liverpool's manager exactly a year ago and Ian Rush, the club's record all-time scorer, said on Monday he thought the team had improved beyond recognition under the Scot's influence in the last 12 months.
"If you look at Liverpool Football Club when Kenny took over compared to where it is now, there's a massive difference," he told the club's website on Monday.
"With Kenny it's all about the club. You win nothing as individuals, it's all about the team. The squad is so much stronger than it was a year ago. The expectations are very high and that can take some getting used to... over the past year there's been real progress. We have become a force again."
