The United boss suggested that Dowd could not keep up after booking five of his players during the match.
The 71-year-old also admitted that it was a tough game, but thought that United could have won.
"Arsenal set off at a fantastic pace, very aggressive and lots of tackles," Ferguson told Sky Sports News. "The referee couldn't keep up at that point.
"When we had a foul, he booked us straight away. We have five players booked. We have got probably the best disciplinary record in the country. For Manchester United to have five players booked, I don't think that is right.
"We expected a tough game, and we got a tough game. Arsenal are fighting for the Champions League, but in fairness, once we had scored, if they [the players] had taken one or two of their chances, we would have won quite comfortably."
United have already won the Premier League this season, but the draw means that they cannot beat Chelsea's record points total of 95.