“With Sonny, I sent him a message after the surgery,” Conte told reporters after the defeat.
“Sonny was really, really disappointed with this situation but I hope for him to recover very well and to play in the World Cup because I was a player and I know the importance of the World Cup.
“He missed us tonight. I’m confident that he can come back quickly and play in the World Cup. He’s not in hospital now, he’s home.”
Son captains South Korea and has scored 35 goals in 104 games for his country since making his international debut in 2010.
He is one of several players to have suffered injuries ahead of this month’s World Cup, with stars including the France duo of Paul Pogba and N’Golo Kante, Portugal‘s Diogo Jota and England‘s Ben Chilwell already ruled out of the tournament.
Conte also admitted he was “disappointed” with fans who booed his team off at half-time when they found themselves two goals down against Liverpool.
“First of all I think we have to show a great respect all the time for our fans,” Conte said. “They are our fans and they pay their tickets.
“At the same time, if you ask me if I was a bit disappointed [about the booing], yes. Because it’s important in every moment to be honest and I think I always continue to repeat, we have just started a process.”
Information from Reuters contributed to this report.