In the 89th minute, Richard Keogh went down inside the area and a penalty ensued from which Lukas Jutkiewicz scored to give City a point.
"I'm stunned at the refereeing decision for the penalty," said the Watford manager to the Sporting Life.
"I asked Trevor Kettle what level he'd [Stewart] refereed at and it's Conference level, so to come into a game today and have to referee at Championship level and give a decision like that, that obviously means I'm a bit upset.
"I've watched the DVD three or four times and there's no pull in there. There's an awful lot of bodies in that area and he sees someone diving thrown his hands up.
"Again, it's the old one where you can tell when somebody's falling, whether they're falling to break their fall or they've got two hands above their head and the boy had two hands above his head and, again, someone with more experience would have noticed that."