The result - their third consecutive victory in the competition - means that the Foxes need just one more win to progress into the last 16.
In contrast, Leicester are struggling to successfully defend their league title as they currently sit 13th in the table, 11 points behind leaders Manchester City after winning just two of their eight games.
"It was a tough match [against Copenhagen]," Ranieri told BT Sport. "We knew that very well, it was a strong team, very well organised, very difficult to beat them, but it was good. In the first half we played so-so. It was difficult to go through the lines but in the second half was much better.
"When you are playing in the Champions League your mind is more concentrated, you are more focused on the match. You lose something when you play in the league. But I hope we can change this soon. We cannot continue in this way. Our goal is to change our concentration in the Premier League."
Leicester's next league game is against Crystal Palace on Saturday.