Fans threw plastic cups and other objects at Biraghi as he prepared to take a corner during the match in Prague and he had to receive medical attention after being struck on the head.
The Hammers are through to a European club competition final for the first time in almost half a century, in which they will face Italian side Fiorentina in Prague on June 7.
"I am happy, because we won a cup that we wanted, to confirm what we did last season. Fiorentina are a quality team who caused us a lot of problems."
The Italians made their first European final in 33 years and will face West Ham United in the showpiece match in Prague on June 7 after the Londoners beat AZ Alkmaar in their semi-final.
The Swiss Super League side are now in a solid position to become the first team from their country to reach a European final.
Fiorentina have appointed Giuseppe Iachini as head coach to replace Cesare Prandelli.
Amadou Diawara struck late to earn AS Roma a 2-1 win at Fiorentina on Wednesday that keeps them in the hunt for a top-four finish in Serie A.
After impressing in a starting role for Arsenal in their 3-0 win over Fiorentina on Saturday, 17-year-old Bukayo Saka said he is ready to “take on the world” as part of an exciting next generation of talent.
Vincenzo Montella returned for a second stint as Fiorentina coach on Wednesday after the Serie A club named him as their replacement for Stefano Pioli who quit in acrimonious circumstances on Tuesday.
AS Roma coach Eusebio Di Francesco is not contemplating resigning after his team continued their roller-coaster season with a 7-1 defeat at Fiorentina in the Coppa Italia quarter-finals.
West Ham United midfielder Edimilson Fernandes has completed a season-long switch to Italian team Fiorentina, the Premier League club said on Monday.
Astori died of what authorities said was cardiac arrest in his hotel room ahead of a league game against Udinese.
Defender Vitor Hugo's thumping header gave Fiorentina a 1-0 win over Benevento in an emotional Serie A encounter at the Artemio Franchi stadium in Florence
Fiorentina coach Stefano Pioli paid an emotional tribute to Davide Astori on Saturday as his team prepared for their first match since their captain died suddenly last Sunday.
Thousands of fans and dozens of players turned out on Thursday to say goodbye to Fiorentina captain and Italy international Davide Astori, who died suddenly at the age of 31
Astori was found dead in his hotel room on Sunday in Udine where Fiorentina had been due to play Udinese.
Italian public prosecutors are to open proceedings to determine whether the sudden death on Sunday of Fiorentina's Astori could be considered as manslaughter.
Fiorentina captain Davide Astori died of a sudden illness on Sunday morning at the age of 31, the club said, leaving Italian football in a state of shock.
Juventus ground out a 2-0 win at Fiorentina after the hosts had a penalty revoked in another contentious incident involving the video replay system (VAR).
Napoli refused to take advantage of the result of ‘derby d`Italia’ after a draw with the same result (0-0) against Fiorentina.