The Whites led the fourth-round tie through a 26th-minute strike from Pablo Hernandez, before Leicester turned the game on its head with a few goals of their own.
Leeds boss Christiansen insists that his second-tier side can hold their heads up high, however, having given the 2015-16 Premier League champions a run for their money at the King Power Stadium.
"We knew about the quality of the Leicester team and I am proud and happy about the performance of the team, especially in the first half," he told reporters.
"We conceded a goal shortly after our goal and maybe if we could have kept the lead until half time then who knows? But we are realistic about who we played against. Ours was a performance of a lot of work and I can't complain."
Leeds turn their focus back to Championship action over the next six days, with back-to-back home games to come against Sheffield United and Derby County.