"It's important for the squad to have minutes to play, those who are not playing in the Premier League and Champions League. We played a very good game and deserved to win," BBC Sport quotes Pellegrini as saying.
The Chilean went on to say that his side has not been handed an easy quarter-final tie, admitting that he is expecting a "difficult" match against Leicester.
"I'm not thinking it's an easy tie, Leicester continue in this cup because they beat Fulham and that is not an easy team so we suppose we will have a very difficult match and if we want to win we will have to play very well," he added.
The League Cup quarter-finals will be played over the week commencing December 16.