Essien gave the ball away after only 13 seconds of the game, allowing Jay Rodriguez to put the Saints in front.
"Everybody makes a mistake," said Mourinho, according to The Metro.
"Strikers they miss goals, goalkeepers they make mistakes, midfield players, they lose balls, especially when they try to play. And he tried to play. It was a back pass and they scored the goal.
"He had a very normal performance. He played a part in the stability the team had in the first half, but one yellow card for 45 minutes is a long time."
Chelsea find themselves in second place in the Premier League table following their victory.