"It's not easy, and I think that we are lucky because we have [Ethan] Ampadu, we have [Andreas] Christensen, we have [Hudson-Odoi], so we are lucky".
Quizzed on the possibility of signing a new striker, he made it clear the responsibility lies with owner Roman Abramovich, saying: "It depends on the board, not on me". I have to try to improve my players in the offensive phase. "I think we played a very good match for 80 metres of the pitch, then we were in trouble in the last 20 metres".
Giroud limped out of Chelsea's 1-0 win over Crystal Palace on Sunday, leaving the unconvincing Morata as their only recognised striker.
Morata has played so badly this season that Sarri had used Belgian winger Eden Hazard in the central forward's role recently rather than turn to the Spaniard, who managed only seven goals this term and none in the league since November 4.
On his recall, the former Real Madrid star looked completely bereft of touch and confidence.
Hudson-Odoi's reservations about signing a new deal at Chelsea relate to the question of consistent first-team opportunities, and Sarri admitted it is hard to balance the developmental needs of the club's talented academy stars with his primary responsibility to keep his team winning.
The boos rang out at full-time as Cesc Fabregas, who came on as a 68th-minute substitute for his 500th club appearance in English football, was waving to the home fans.
Chelsea is now fourth in the table, three points ahead of Arsenal and six up on Manchester United for the last Champions League spot.
The Ivory Coast worldwide has attracted the attention of several clubs in Europe with his performances for the Rossoneri and some of them are keen to snare him away from the San Siro.