The Foxes started the match brightly just as they did at home to Manchester United the previous week, but they somehow found themselves behind after 15 minutes of the match when Jordan Thorniley volleyed home a George Green set piece.
City responded well to the set back and were able to carve out numerous openings against their more experienced opponents though.
Trevor Peakes’ side were getting plenty of joy on the flanks, but the finishing didn’t match the quality of the build-up when a one-on-one was put over the crossbar before youngster Kyle Bailey had an excellent effort saved by the Everton ‘keeper.
Lithuania Under-21 international Simonas Stankevicius then struck the upright with another great effort at goal, but it just wasn’t to be for the Foxes as the home side held out for a narrow victory.