The Ghanaian's wayward back pass gifted Jay Rodriguez the chance to put the visitors ahead, but Mourinho insists he was satisfied with Essien's performance.
Essien's wayward back pass allowed Jay Rodriguez to put the visitors in front just 13 seconds into the match and put Mourinho's home unbeaten run in the Premier League under threat.
But Chelsea rallied after the break and goals from Gary Cahill, John Terry and Demba Ba ensured no more ground was lost on league leaders Arsenal.
After the match, Mourinho insisted he was pleased with Essien's performance, despite replacing him with Ba after just 45 minutes.
"Everybody makes a mistake," Mourinho told reporters. "Strikers they miss goals, goalkeepers make mistakes and midfielders lose the ball, especially when they try to play, and he tried to play. He had a very normal performance. He played the same way Mikel plays or when Luiz plays in midfield.
"He played his part in the stability of the team, but one yellow card for 45 minutes is a long time. I had to take one [of him or Ramires off]. But he's my man, he's a Chelsea man and it's no problem."
Mourinho also paid tribute to the way his Chelsea side reacted to the early setback and exploited his tactical shift to a more orthodox 4-4-2 to turn the game on its head.
"In the first half we played very well," he added. "We played with balance, calm, no panic, no silly decisions, no mistakes, not risking a lot. When I had to change Oscar it looked a defensive change, but it was a change to prepare the second half. I had to play with two strikers, so we changed for the 4-4-2 and gave Southampton a different game they didn't expect and couldn't deal with."
Mauricio Pochettino, meanwhile, bemoaned his side's slackness from set pieces as the decisive factor in the Chelsea comeback.
"The game changed when we scored the goal, but even after that we competed very well," he said. "In the second half until 1-1 was our best spell attacking football, but then we conceded two goals from set pieces and that's a mistake that can't happen.
"They were soft goals we shouldn't have conceded and that decided the game in the end."