The silence had been arranged as a mark of respect to the 96 football fans who died in the Hillsborough disaster 23 years ago but was marred by booing and singing from a small section of the Blues' support.
Players from both sides also wore black armbands as a joint tribute to Italian footballer Piermario Morosini, who tragically died from a cardiac arrest on the pitch during Livorno’s match against Pescara on Saturday.A statement from the club read: "Chelsea Football Club is extremely disappointed that a very small minority of fans embarrassed the club today by not honouring the moment's silence before kick-off.
"Chelsea FC believes all moments of respect should be honoured and today we pay our full respects to all those that suffered as a result of the Hillsborough disaster 23 years ago."
Roberto Di Matteo's side ran out 5-1 winners on Sunday to set up a clash with Liverpool at Wembley on May 5.
The Italian boss also later expressed his sadness over the disruption, saying: "We are extremely disappointed that a minority chose not to respect it."