Chelsea coach Jose Mourinho was unhappy with the refereeing decision. Chelsea were denied two stone wall penalties, with United defenders Rojo and Smalling head locking Chelsea defenders John Terry and Ivanovic during a corner.
Later Ivanovic was sent off for his offense on Januzaj and was shown second yellow card. The game saw 8 yellow cards as referee Phil Dowd was on a card happy sphere.
"The red card, I saw that coming," said Mourinho after the 1-1 draw.
"If I have to speak about [that] I have to speak about the penalty Ivanovic should have been given."
But he added: "I don't want to speak about the penalty on Ivanovic [when the Serb appeared to be wrestled over in the area by Chris Smalling] and the accumulation of yellow cards [for Chelsea].
"I don't want to speak even about throw-ins. If I want to speak I will speak too much - you know I will speak with my heart and get into trouble."
Chelsea will be charged £25000 for their 6 yellow cards in the game.
But Chelsea who lead Southampton who are second on the table by four points take on their closest rivals QPR in the league next.
Jose Mourinho was overall happy with his sides performance against United, and was quoted saying
"Old Trafford is one of the most dangerous fixtures we have. The result is not the result we want, but the way we performed means we don't need to look to others," he said, with Chelsea six points ahead of City and four clear of second-placed Southampton.
"Don't forget we have also played away at Manchester United and Manchester City.
"We are going in a good direction."
After an even first half, Chelsea dominated, with Eden Hazard going close before Drogba scored.
"The second half was much better," added Mourinho.
"From the start of the first half we showed we wanted to win. In the second half we didn't give them the chances they wanted. To come here to Old Trafford the way we did - it was fantastic by my boys."