Newcastle confirmed on Saturday that Pardew had been released from his contract in order for the 53-year-old to take over at Premier League rivals Crystal Palace.
A large section of Newcastle fans have long been calling for Pardew's departure, yet they were unable to celebrate a victory on the day of his exit.
The visitors produced a toothless attacking display at the King Power Stadium, and were punished for their lack of creativity with a third successive third-round exit.
Caretaker boss John Carver did see a Remy Cabella strike controversially ruled out for offside, but Newcastle rarely threatened and were eliminated courtesy of a goal from Leonardo Ulloa.
The Argentine forward's 39th-minute header settled the tie in Leicester's favour, perhaps giving the Midlands club confidence that they can lift themselves off the bottom of the Premier League and move towards top-flight survival.
Newcastle had the better of the opening stages in terms of possession but were unable to create any goalscoring opportunities of real note as the game got off to a dour start.
Leicester, who handed a first-team debut to Wales Under-21 forward Tom Lawrence, were forced into a change in the 26th minute as midfielder Esteban Cambiassio limped off with a right thigh injury to be replaced by Marc Albrighton.
The visitors looked to have taken the lead in the 32nd minute with the first real chance of the game, attacking midfielder Cabella finishing off an excellent Newcastle counter-attack only to be denied by a late offside flag.
And Leicester capitalised on Newcastle's misfortune seven minutes later as Ulloa broke the deadlock.
Ulloa headed Anthony Knockaert's cross in off the underside of the crossbar following a short corner from Albrighton.
Leicester carried the momentum from that goal into the second half and Ulloa went close to doubling his tally in the 54th minute as he turned a corner narrowly wide of the post.
Nigel Pearson's men continued to craft the better openings, with Chris Wood then brilliantly denied by Newcastle goalkeeper Jak Alnwick.
Wood met a superb cross from Albrighton with a diving header, yet Alnwick flung himself to his right to preserve the one-goal deficit.
Alnwick was called into action again to deny Jamie Vardy late on before Mike Williamson almost conceded a second by heading against his own bar as Newcastle exited England's most prestigious cup competition with a whimper.
