Alessandria brought more than 15,000 fans to the San Siro stadium for their big night but reality quickly bit when the five-time winners went one up after 20 minutes.
Frenchman Menez, back in form after spending much of the season injured, controlled the ball on his chest before smashing home a superb opener.
Romagnoli turned in a half-volley soon afterwards before Menez made it 3-0 by halftime with his clinically-taken second.
The rout continued near the end when Romagnoli had a fourth goal confirmed by goal-line technology and Mario Balotelli scored in the dying seconds.
Milan will now play either Juventus or Inter in the final, with Juve in seeming command, holding a 3-0 advantage from the first leg before the return in Milan on Wednesday.
(Reporting by Ian Chadband in London, editing by Pritha Sarkar)
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