Last week, the East Midlands outfit announced that they had sacked Craig Shakespeare after a poor run of form, but caretaker boss Michael Appleton guided Leicester to a 2-1 win over Swansea City on Saturday.
The Foxes are likely to make changes for Tuesday's clash with Leeds, but Morgan has stressed the importance of a win over the Championship outfit.
The 33-year-old told the club's official website: "We've done well so far in the competition. We saw off Liverpool in the last round and we've got Leeds next so we want to progress.
"It's a good game for us and it's an ideal opportunity because we're at home, so hopefully we can get that win.
"We got a win today (Saturday) and if we get another win on Tuesday, it will build momentum and hopefully we can climb up the [Premier League] table too."
Leicester have not reached the quarter-finals of the League Cup since winning the competition in 2000.