He felt Michael Essien fouled Ryan Giggs in extra time, stopping the winger having a chance on goal.
Ferguson said: "It's a penalty. To lose a game and see that is disappointing.
"I think the pressure Jose Mourinho put on the referee before the game has certainly worked and I'm disappointed at that."
In the build-up to the game Chelsea boss Mourinho had called for referee Steve Bennett not to be fooled by any diving or 'provocative tactics'.
Essien challenged Giggs as the Welshman slid in to try and get on the end of a Wayne Rooney cross.
Giggs' effort was straight at Chelsea keeper Petr Cech, who appeared to carry the ball over the line as the United player collided into him.
Ferguson added: "It's a penalty kick. Then the goalkeeper's spilled the ball behind the line.
"I think it would have been a difficult one for the linesman to call but the referee should be in a better position.
"We couldn't see where we were but when I see it now it's a penalty."
Giggs felt that Bennett the referee should have given a goal.
"It was clearly over the line - that's what I was asking for. I could see it was over the line and he didn't give a free-kick so it was a goal.
"I felt I was getting to the ball quite comfortably and felt someone touch my leg.
"But I was claiming for the goal not the penalty.
"We're disappointed obviously. The big decisions didn't go for us and if you don't get the big decisions it is going to be hard for you.
"The referees are picked on merit and how they perform throughout the season.
"The FA Cup is a big occasion and you want the referees to get the big decisions right. They are only human and sometimes they get them wrong but in the Cup final you hope they get them right and today they didn't.
United assistant Carlos Queiroz also felt that Bennett's decision-making was affected by Mourinho's comments.
He added: "In some moments we created the better opportunities and we had chances.
"But unfortunately come the crucial moment in the game the referee missed the most important decision but we are not surprised by that.
"It is a clear penalty, there is no doubt about that. We are not surprised because after the pressure of the last 15 days it is natural the referee under pressure is not able to make the crucial decision of the game.
"The more pressure you put on referees the more it seems like some teams and some managers become compensated in the game because nobody does anything about that.
"We could see that pressure gave a big reward to Chelsea."
Ferguson blamed tiredness for his side's below-par display in the first FA Cup final back at Wembley.
He added: "There was a bit of tiredness. The number of games they played eventually gets to them. It was the same for both teams but I think in two or three positions we were tired.
"The pitch was slow, maybe that didn't help but, from our point of view, we were tired.
"There was nothing between the two sides. Neither deserved to win or lose and we are disappointed we have lost.
"It has been exceptional what my players have been through - we just couldn't cross the line."
Giggs added: "We played well. It was two very good teams but we probably edged it with possession and chances."