The Red Devils won the game 1-0 with Dillon Hoogewerf's header securing the result and setting up a home tie against Wigan Athletic in the next round of the competition.
17-year-old Mejbri played the full 90 minutes at Old Trafford but was subject to chants from the 1,400-strong travelling support calling him "a s**t Sideshow Bob" in reference to his similarly distinctive hairstyle.
The midfielder responded via Instagram after the match, posting a photo of the Simpsons character smirking.
The caption, which is partly written in French, reads: "I admit that there is a small resemblance," followed by two laughing emojis.
Mejbri also wrote: "Good win tonight 1-0 vs Leeds in the FA Youth Cup, through to the next round."
He joined United last summer from French side Monaco, commanding a fee of around £4.5m with the potential to rise to £9m.
He is held in very high regard at the club and has been compared to the likes of Roy Keane and Bryan Robson by 'Class of '92' graduate Nicky Butt.
Butt, now head of first-team development at United, told Manchester Evening News that he sees Mejbri as a "leader".
"The way he plays football is 100mph, he's non-stop running up and down," he said.
Mejbri has created three goals in five matches for United's under-23 side this season and will be looking to wiggle his way into Ole Gunnar Solksjaer's first-team plans within the next few seasons.