The two sides battled to a 2-2 draw at Wembley before the Blues went on to win 4-1 in the shoot-out.
Nani opened the scoring for United in the 10th minute with a long-range effort across goal that evaded goalkeeper Petr Cech.
Ricardo Carvalho headed home the equaliser for Chelsea early in the second half before an effort from Frank Lampard gave the Londoners the lead.
Despite an injury-time leveller from Wayne Rooney, the United boss was disappointed that referee Foy played on in the build-up to Chelsea's second goal, with Patrice Evra lying down injured.
"I think the referee clearly saw it," Ferguson told Sky Sports.
"He's elbowed him in the face and he's clearly in line with the actual incident and I'm disappointed because he stopped the game twice before that for fouls, with players lying down.
"When Ballack was lying down he got up within seconds. He thought it was a serious foul but you've seen Ballack. That incident cost us the game really."
FrustrationFerguson added: "I asked the referee, he said he thought it was a serious incident, and he thought the player needed treatment, whereas he [Ballack] was up right away.
"Once he has done that, I do not understand why he has not stopped the game when Evra is lying down?
"With a replay you can see Ballack has elbowed the boy, and if the referee had seen it properly, it is a red card.
"It is hard to blame the Chelsea players, because it is a professional game.
"But it is making it very difficult for referees [to know] when players are acting to get the game stopped.
"It is an area I am concerned about and we have got to find a solution to that part."
ResponsibilityFerguson continued: "If we are putting the responsibility back on the referees and they are deciding when the games should be stopped, then fine.
"He has got to be correct in that respect. As we saw today, he never got it quite right. You have to be consistent."
Manchester United dominated the early stages of proceedings at Wembley, but the Red Devils boss was frustrated at the way his side let Chelsea back in the game
He said: "We played well for a lot of the game and we should have put it to bed in the first half. Their first was a poor goal from our point of view, we should have defended it better but Chelsea at that point came into the game and were controlling it.
"The second goal as we saw shouldn't have been allowed but once they got that goal Chelsea weren't losing the game, I think they were in control, they got the equaliser and then penalty kicks - well we've never been that good at penalty kicks."
Asked whether he was concerned that some players feigned injury to get the game stopped, Ferguson said: "Well we've seen it time and time again.
"I don't think there's any question about that, but we've got to a level now where it's being used now as a professional way to get the game stopped."