Manchester City remained on course for the Quadruple after a dramatic penalty shoot-out win – even if boss Pep Guardiola ruled it out.
Keeper Claudio Bravo was City's Carabao Cup match-winner again, saving the decisive spot-kick from Riyad Mahrez to send Guardiola's side through to the semi-finals.
The victory keeps City, who have an 11-point lead at the top of the Premier League, on course for a clean sweep of all four trophies to eclipse local rivals Manchester United's Treble success of 1999.
But Guardiola dismissed any suggestion City – who have also been installed as favourites for the Champions League - can win every trophy available to them this term.
“That's unreal, that's not going to happen,” said Guardiola. “What we are living isn't real. I'm not even thinking about that.
“Winning 16 games in a row in the league, qualifying for the Champions League knockout stage two games before we finish the group stage, then coming here and winning with young players, it's not normal.
“In football you drop points and you lose competitions, but of course we're in the semi-final now, but I'm not thinking about how many titles we can win.
“And in the process, you don't need to wait until you've won titles to live and enjoy the moment. We have a good reason to enjoy it and we want to enjoy it with our fans.
“It makes no sense to wait to win to be happy or unhappy, and we did it again, especially today, because we knew it was difficult against Leicester with a lot of young players.”
Keeper Claudio Bravo was City's match-winner in the competition again after making two saves in a shoot-out against Wolves in the previous round to send the Blues through.
Bravo saved Mahrez's spot-kick after Jamie Vardy – who had scored from the spot in the 97th minute to force extra-time – also missed in the shoot-out
City were moments away from booking their semi-final place when ref Robert Madley awarded Leicester a with a minute of added time left for a foul by Kyle Walker on Demarai Gray.
Vardy scored from the spot, cancelling out Bernardo Silva's 26th-minute opener to send the tie into extra-time, with City holding their nerve in the shoot-out to progress.
Guardiola added: there were no complaints from the players in extra time about how it was unfair that they had scored a late goal.
"The way we had to react was not easy, we were tired, we had a lot of young players.”
Guardiola said he did not know if David Silva - left out of City's 4-1 win over Tottenham for personal reasons - would be back for Saturday's game against Bournemouth.
"I don't know," said Guardiola. "It's personal reasons. But I prefer not to make a statement because it's a personal matter."