The Reds boss felt that Dowd was unable to keep pace with the game and was over the top with his bookings of eight players.
From the kick off Arsenal flew at United and applied massive early pressure, which ultimately lead to Theo Walcott netting the opening goal after just two minutes.
After that the game continued at a pretty frantic pace until United equalised just before the half time break through Robin van Persie.
Yellow cards were shown to United's Phil Jones, Rafael da Silva, Jonny Evans, Antonio Valencia and Van Persie; while Arsenal also saw three of their players go into the book.
Speaking to Sky Sports after the game, Ferguson said: "Arsenal set off at a fantastic pace, very aggressive and a lot of tackles.
"The referee just could not keep up at that point. When we had a foul, he booked us straight away. We had five players booked.
"We have got probably the best disciplinary record in the country. For Manchester United to have five players booked, I do not think that is right."