Davies will now miss the first game of the Bantams' play-off campaign.
"Andy D'Urso is a very experienced referee and he was stood very close to the incident," assistant manager Parkin said.
"Not for one minute did he look as though he was going to give a foul but he has then got involved with his own linesman who was further away. We were disappointed with that.
"Andrew was then told in no uncertain terms at half-time that he had to be whiter than white and not to get involved in anything but he has then had a silly sending off which means he will miss one of the games next week which has put a slight cloud over the day."