(CNN) -- Zlatan Ibrahimovic scored the only goal of the game as Inter Milan beat Sampdoria 1-0 in their Italian Cup semifinal second leg at the San Siro, but it was not enough to prevent the visitors reaching the final 3-1 on aggregate.
Ibrahimoviv scored the only goal at the San Siro, but Inter Milan have still bowed out of the Italian Cup.
The Swedish international striker volleyed home a superb strike in the 27th minute -- although he was unfortunate not to double Inter's lead on the night when his lob hit the post 10 minutes later.
Sampdoria had their chances to take something from the game with Antonio Cassano and Giampaolo Pazzini both denied by good saves from Inter goalkeeper Julio Cesar.
The evening ended badly for Inter with defender Marco Materazzi sent off in the final minute.
However, their 3-0 first leg victory ensured Sampdoria were always in the driving seat and they now move forward to their first final since 1994 -- when they beat Ancona to lift the trophy.
Sampdoria's opponents in Rome on May 13 will be Lazio, who completed a 4-2 aggregate win over Juventus on Wednesday.
The shock semifinal results saw both the top two teams in Serie A crash out and meant Inter's run of four successive final appearances, winning in 2005 and 2006 and losing in 2007 and 2008, have come to an end.
However, the defending Serie A champions still look poised to retain the Scudetto as they lead Juve by 10 points at the top of the table with just six matches remaining.