Liverpool will have some challenging weeks with many disadvantages like injuries and absence of key players because of African and Asian Cups. This winning will help them to have some different options to prepare for a second-leg match with Fullham 2 weeks later on 25 January. League Cup is not too important with them compares to other big competitions, Premier League and Europa League.
With some injuries and risk of injuries from Salah and Endo because of international duties, Klopp will have to build up careful plan for Liverpool in next two months, this month and one month later when Salah and Endo returns to Anfield. Even those players return without injuries, he will have to give them one or two weeks to recover.
I hope Liverpool can overcome this challenge despite a few absentees and international duty, perhaps the hardest opponent over the next month will be Arsenal away but I think Klopp will devise the best strategy as long as they have little trouble.
The EFL Cup is not the least bit important, if Klopp is able to win this title then great, if not no big deal their focus will only be on the Premier League and Europa League.
That is what Klopp and his fans are worried about, they hope Salah after the competition does not have injury problems, because he is a player who is quite reliable for Liverpool in important matches.