The young Blues were knocked out of the competition by a Premier League club at the third-round stage for a third successive season.
Dan Smith put the young Blues in front midway through the first half but Kairo Edwards-Smith’s double – his second an extra-time winner – left Mark Kelly’s troops devastated after they missed a number of golden chances.
Leicester dominated the early stages and Pompey stopper Jack Collins made two top-drawer saves.
On seven minutes, the Blues goalkeeper denied Simran Thandi’s sliding effort from point-blank range before tipping Edwards-John’s curling effort over the bar 11 minutes later.
The hosts grew into the game and in the 19th minute, they engineered their first real move.
Matt Mayes looked destined to score only for Calvin Ughelumba’s last-ditch challenge to take the ball off the Pompey captain’s boot.
Kelly’s troops had their first effort on goal when Smith drilled a right-footed free-kick wide on 22 minutes.
The second-year scholar then headed over the crossbar four minutes later before opening the scoring in the 32nd minute.
Joe Dandy whipped in a free-kick from the left and referee Adam Penwell pointed to the penalty spot after seeing a foul on Mayes by Lukas Husek.
Smith stepped up to take the kick and kept calm under pressure to slot his effort into the bottom left-hand corner.
Pompey continued to defend gallantly and went into the interval with a 1-0 lead.
But the King Power Stadium outfit were level just 71 seconds after the restart.
The Foxes worked their way into Pompey’s box and Edwards-John calmly slotted his right-footed effort beyond Collins.
The Blues didn’t let their heads drop, though, and had two decent chances soon afterwards.
On 52 minutes, Smith bent a left-footed effort just off target and two minutes later Leon Maloney blazed wide from inside the box.
In the 66th minute, Smith had another decent chance.
Freddie Read nicked the ball in midfield and Bradley Lethbridge teed-up the Warsash talent but he failed to hit the target.
Pompey continued to have the better chances with a Lethbridge effort heading for the far corner before it was blocked by Thandi on 72 minutes.
Leicester had a gilt-edged chance to nick the game in injury-time.
Following a swift counter-attack and with the goal at his mercy, Conor Tee got his footing all wrong and the Blues deservedly took the game into extra-time.
The hosts’ intensity did not drop but they fell behind for the first time in the 99th minute.
Edwards-John cut in from the left after a mazy run and drilled a right-footed shot inside the far post beyond a helpless Collins.
Pompey pushed hard for an equaliser but could not find a way through.
Nevertheless, it was a performance all of the young Blues could be proud of having had the lion’s share of possession and chances.