Kirsten Otchere scored a second half goal for the Foxes but Cooke's late strike saw the Cottagers take the points at LCFC Training Ground as the young Foxes sit seventh in the U18 Premier League South Division.
Heading into the fixture off the back of a Premier League Cup defeat to Leeds United, it was the visitors who took the lead through Basmil Lubega before Otchere levelled the scores just over the hour mark, netting his second in as many games.
Heading into additional time level with title chasers Fulham, it was heartbreak in the final moments for Leicester as Cooke stole the points in Seagrave, taking the London outfit to second in the standings.
With eight points from six games, City are back on the road on Saturday morning when they take on Crystal Palace, currently one point behind, in Kent at Crystal Palace Training Ground for an 11am BST kick-off.
The details...
City: Marson; Aluko, Gray, Diallo, Khela; Page (Lawrence 46'), Dyke; Owusu, Otchere, Omobolaji; Hutchinson (Aideed 70').
Unused subs: Adedeji, Daniels, Hibbins.
Goal: Otchere 67'.