Scott saw his sides half time lead wiped out by two second half goals he felt should have been ruled out, as the Millers battled with only ten men after Marcus Marshall's dismissal before the break, which the manager admitted was the right decision.
The gaffer told the press afterwards: "The first goal shouldn't be allowed as Conrad's (Logan) arm is held at the set piece, I pointed it out to the ref at half time what they were doing but he took no notice in the second half either."
Former Miller Ian Sharps equalised Lewis Grabban's penalty, then the Shrews won it with a spot kick of their own. Nicky Wroe slotted in after Marvin Morgan tumbled in the box to knock the Millers out of the FA Cup at the second round stage.
Scott added his frustrations, saying: "Morgan's pulled Tom (Newey) back then just fallen over, it's not a foul. But the ref will go and ref another game next week no doubt and a third round game too when we won't be there, we at least should have had a replay.
"It is a tough place to come with 11 men but we just didn't start the game well enough, we were too deep and we didn't play with the positive nature that we normally do. We let them get on the front foot and then we got the goal which gave us a little lift, but the second half is a completely different game because of the sending off. Marshy's caught him from the side and it is a sending off.
"In the second half we restricted them to long range efforts from the middle of the goal which we were comfortable with, we had several chances to get the ball into the box and create problems. They had a lot of possession, which we expected, and the lads worked hard but sometimes you just cannot legislate for what happens."