Albion defended resolutely throughout, restricting the hosts to few goal-scoring chances.
The Seagulls occasionally posed a threat, themselves, on the counter attack, with the offside flag denying Andi Zeqiri his first goal for the club.
After Cengiz Under also saw his goal ruled out for offside, it looked like the tie was heading for extra-time.
However, Brighton were dealt a cruel blow with just seconds remaining, when Iheanacho turned in Youri Tielemans' cross.
Scroll down and click through to see how journalism student Sam Cox rated Graham Potter's men out of ten.
Photos via Getty Images
1. Christian Walton - 7
The former FA Cup quarter-finalist with Wigan Athletic in 2018 was rarely called into action during the 90 minutes. However, Walton looked assured whenever Leicester City did threaten, with his best moment coming when smothering Jamie Vardy when the former England international looked certain to score. Couldn't prevent Iheanacho from scoring from five yards out in the last minute of injury time.
2. Lewis Dunk - 7
Another consistently high performance from Albion’s captain was helpless in preventing the winning goal in injury time.
3. Michal Karbownik - 6
A relatively quiet debut from Karbownik, but never looked out of his depth. Provided a creative spark during the first half, but became less influential as the match grew longer.
4. Dan Burn - 5
May take the blame for the hosts' winner after allowing Iheanacho to sneak in and head home. Always a threat down the left-hand-side, Burn often found space between the Foxes’ centre-back and full-back. Unfortunately for Albion he struggled to pick out the onrushing attackers when whipping the ball across goal and had his blushes spared after knocking the ball to Cengiz Under who slotted home, only to see his effort ruled out for an offside in the build-up.