The Portuguese manager ranted for seven minutes in response to a single question from Sky Sports.
Much of it focused on referee Robert Madley's refusal to give a penalty when Falcao went down under a challenge from goalkeeper Maarten Stekelenburg.
Chelsea claim Jose Mourinho 'has their full support'
Mourinho said of his side's poor start to the season: "When you are so down, I think it's time to be a little bit honest and to say clearly the referees are afraid to give decisions for Chelsea.
"The result was 1-1 when it was a huge penalty, and, once more, we didn't get one.
"And the penalty was a crucial moment in the game with the result 1-1.
"And, I repeat, if the FA wants to punish me, they can punish me. They don't punish other managers, they punish me, but it's not a problem for me."
He later added: "And this penalty in this game today is more than crucial and you know why? Because my team in this moment ... the first negative thing that happens, the team collapses, the team mentally and psychologically is unbelievably down."
Graziano Pelle celebrates after scoring the third goal for Southampton.
Image credit: Reuters
The FA alleges his comments "imply bias on the part of a match official".
The defeat by Southampton means Chelsea have lost four of their opening eight games in the Premier League this season, leaving them 10 points behind Manchester City in top spot and just four points above the relegation places.
But Mourinho also defended his position after the game. He added that if Chelsea sack him, "they sack the best manager this club has had".
He has until 6pm on Thursday 8 October 2015 to respond to the charge.
Mourinho: There's only one thing that would make me resign from Chelsea
John Terry gives Chelsea manager Jose Mourinho his public backing