Seedorf's Milan suffer Italian Cup KO
Dutch former football player and newly appointed AC Milan coach Clarence Seedorf (C) waits for the begining of the Italian Serie A football match AC Milan vs Verona at San Siro stadium in Milan on January 19, 2014 - by Marco Bertorello
Mario Balotelli gave Milan a sixth minute lead before they were pegged back by a 41st minute penalty converted by Colombian Luis Muriel.
Udinese dominated the second half and grabbed the winner in the 77th minute through Uruguayan star Nico Lopez.
Udinese will face either Fiorentina or Siena in the semi-finals.
The defeat also severed a potential European route for AC Milan who are already 30 points behind leaders Juventus in Serie A.
Their last hope of playing in Europe next season will depend on their progress in this season's Champions League where they face Atletico Madrid in the last-16 next month.
Balotelli was on target early on Wednesday when he converted a cross from Valter Birsa, preferred in midfield by Seedorf to Brazilian star Robinho.
But Udinese, who are just three points above the relegation zone in Serie A, won a penalty when their Swiss import Silvan Widmer was fouled by Urby Emanuelson leaving Muriel to slot home from the spot.
Milan keeper Christian Abbiati kept out Gabriel Silva and Muriel late on before Lopez hit the winner within a minute of coming off the bench.
The other semi-final will pit Roma, who beat Juventus 1-0, against either Lazio or Napoli who play on January 29.