Nicolas Anelka grabbed both City goals, the first an unstoppable penalty and the second a rare header, just 3 minutes after Marcus Bent had put Leicester ahead once more.
City put in a gutsy performance but dismal defending prevented them from snatching the win they desperately need.
First Sun Jihai allowed Bent in to cross for Dickov, who turned the ball home superbly from a tight angle, just 6 yards out.
Then Richard Dunne misread Callum Davidson's long-ball to leave Bent in the clear to volley past David Seaman from the edge of the box.
City produced sustained attacks after each Leicester goal but often spent too long trying to find the perfect final ball or the perfect shooting position.
Robbie Fowler was twice blocked by Ian Walker before Billy McKinlay's trip on Paul Bosvelt brought about the 27th spot-kick. Despite determined efforts by the away fans to distract him, Anelka fired high to Walker's right.
Shaun Wright-Phillips appeared to be brought down by Ricardo Scimeca straight after the break but Graham Poll refused to award City a second penalty. City were still on top but were unable to make their possession count, creating few clear-cut chances.
Dickov, by now falling over every time a Blue shirt went near him and also lashing, was taken off before he was sent off. The ex-Blue had been frequently booed by his former fans but received applause from all corners of the stadium when he left the field.
Bent then struck against the run of play before Anelka headed in Fowler's right-wing cross. The game was there to be won but the closest City came was in the closing stages when Fowler's right-foot shot went inches wide of Walker's right-hand post.
Kevin Keegan was disappointed that City couldn't snatch a win but was pleased with his men's overall display.
He said: "I think it's a confidence thing now. The spirit and the effort is pretty good but we need a victory and the confidence that will give us.
"It is disappointing but it is understandable. The lads have taken a few knocks but they have kept going."
Kev added: "Things change very quickly in football. Eventually we will start to win games we shouldn't and that is when it gets very nice.
"That is not happening for us now. But we deserve another crack at this tie, and there will be some clubs over this weekend who will wish they had the same opportunity."
City: Seaman; Sommeil, Dunne, Distin, Jihai; Wright-Phillips (Sinclair 80), Reyna, Bosvelt (Barton 80), McManaman (Sibierski 45); Anelka, Fowler.
Subs Not Used: Stuhr-Ellegaard, Macken. Booked: Sommeil.
Leicester: Walker; Impey, Heath, Scimeca (Stewart 55), Davidson; Hignett, McKinlay, Izzet, Scowcroft; Bent (Brooker 85), Dickov (Ferdinand 62).
Subs Not Used: Coyne, Nalis. Booked: Dickov.
Attendance: 30,617.
Referee: Graham Poll (Hertfordshire).