The Blues ran out 3-2 winners at St Mary's Stadium on Saturday despite being two goals down at the hour mark.
"A good win but for me it was important to see the right spirit, the right passion and enthusiasm in the second half," Conte told BBC Sport.
"In the first half we didn't play well but not just that, they put more into the tempo than us. I was very disappointed but we must be pleased by the second half.
"The most important thing is to show in every game the right passion and to fight until the end. We need to finish this season in the best possible way.
"I don't know why the desire wasn't there but the coach is the first person to have the fault. It doesn't matter that we won the game 3-2, it was important to see the right reaction and fight in the eyes of my players.
"Southampton played a good game and took a lot of confidence after their first goal because they were nervous at the start. It was difficult for us to come back so we must be pleased by the desire we showed."
Chelsea are now within seven points of fourth-placed Tottenham Hotspur in the Premier League table.