Wednesday were beaten 2-0 at the home of their League One opponents and missed the chance to set up a fourth-round trip to QPR.
And Jones felt both referee Lee Collins and his strikers were guilty of being too timid.
He said: "He allowed (Dons midfielder) Alan Smith to run the game. At the end of the day he might as well have given the whistle to Alan, because he ran the game.
"I just thought it was too big a game for him. He lost it somewhere along the line and that can happen, so he's had a bad day at the office."
Of his team, Jones said: "We didn't really get many shots in on goal and that was disappointing because we saw plenty of the ball.
"But we didn't seem to want to shoot and that's not like us. We had more than a few chances to get the ball into the box but ended up almost passing it back to the goalkeeper. We need to be more forward thinking.
"I'm disappointed to go out of the cup because we had a chance to go through and the side we put out was good enough to win the game. And I really felt for the fans behind that goal who came all the way down here."