United were at The Academy in Liverpool to face the Premier League Champion's under-23 side on Thursday afternoon, and it was the young Reds who worked their way to a commanding first half lead.
Carlisle started well, when Joe Riley robbed possession before going on a run down the right flank. He whipped the ball into the box but it was too far in front of Kayode.
But it was the hosts who took the lead when they made their way down the left wing, with three players causing an overload. A winding run and clipped ball into the box was tapped into the net from close range.
The Blues kept probing but the lead was doubled on 17 minutes when Farman spread himself to make an initial good save as a striker came through to go one-on-one. The ball spun up off his outstretched hand and a favourable ricochet was poked into an empty net.
United played some good stuff as they tried to get back into the game and a slick move earned a corner as Guy, Reilly and Riley combined. The delivery was met by Kayode but his header looped onto the roof of the net.
Another patient build up from the visitors brought an effort from distance from Birch, but the keeper saw it early and he was able to drop low to gather it in.
The Reds added another before the break, and Kayode went within a whisker from a whipped corner at the other end as he timed his run to perfection. The downward header appeared to be going in but it spun agonisingly just wide of the upright.
An error at the back allowed Liverpool to add a fourth within moments of the second half restart, and that sparked a positive spell from United as they pushed men forward. A run from Riley was followed by a deep cross but Devine could only volley it wide as he arrived late.
Gavin Reilly then split the defence with a neat through ball but a curler from Kayode, as he burst through, was too close to the stopper.
Reilly was on the move again when he was spotted by Toure. A drilled reverse pass from the marauding forward was met by a near post run from Kayode, but his touch sent the ball into the side netting.
Carlisle got the goal their improved display deserved when Max Hunt took a high ball on his chest before nipping it back into the mix. Kayode had peeled off his man and he beat the keeper with a firm and accurate header.
Midfielder Callum Guy almost added to the visiting tally when he got on the end of a decent move, which had involved touches from Bell and Lightfoot and a cross from Toure. His header was on target but the keeper was well positioned.
Carlisle United - Farman (Dewhurst 46), Riley, Hunt (Barnes 85), McDonald, Anderton (c) (Leslie 55), Guy, Devine (Lightfoot 60), Birch (Armstrong 76), Toure, Reilly (Bell 60), Kayode. Sub- Robinson, Day.
Goal - Kayode (63)
Attendance - BCD