The Blues progressed on Wednesday night while their rivals lost with a 2-0 win over Blackburn through goals from Benoit Badiashile and Raheem Sterling.
United and Arsenal lost to Newcastle and West Ham, respectively, with Liverpool also left in the competition but Manchester City and Tottenham have already been knocked out.
Asked whether Chelsea should start thinking about winning the Carabao Cup, Pochettino said: "I think so. We need to think that it is an important competition for us.
"We are not in Europe. That should be an opportunity for us just like the Premier League is and like the FA Cup when we start in January.
"Of course, we need to think that we can win this competition."
Reece James made his first start since August in the win and completed 60 minutes in a positive display at Stamford Bridge.
Pochettino was delighted to see his captain return, who he believes will prove influential with tougher tests against Tottenham and Manchester City to come.
"He is really important, always," said the manager. "When you decide that he's your captain it is important that he stays fit, can play and help the team. He’s an important player for us.
"He’s an amazing player, for me one of the best full-backs in the world. It's unlucky that he only played 70-75 minutes against Liverpool in the first game and until today didn't play.
"The temptation is: 'Okay, come on go and play 90 minutes'. But we need to be careful. Little by little he is going to get fit and cope with the demand of the games."