Jon Rudkin’s side could have taken the lead shortly before half time from the spot but City missed their penalty and allowed the hosts into the game.
Both sets of youngsters created several clear-cut opportunities but failed to break the deadlock and shared the spoils.
It can be considered a good result considering the Hammers won their first game of the season against West Bromwich Albion – a 3-1 away win – and already had momentum going into the clash.
The Foxes, who already have a game in hand on the majority of Under-18 sides following the postponed fixture against Fulham, host Chelsea on Saturday afternoon at Belvoir Drive in a 1pm kick off and could move into the top four with a win.