Robinson said he had seen replays of Smith's aerial challenge with Rory Delap and believes the former Manchester United man's reputation preceded him.
"I didn't even know it was a foul," he said.
"But you see Alan Smith going to try and compete and right away ultimately the referee thinks 'that's Alan Smith, he has tried to do him, sending off'.
"You could see it and, by the way, how quick did he go for his card? It looked like he couldn't wait to do it but if he sticks to his report he will know he has made a big error."
A Chris Dagnall brace and a Marlon Harewood effort saw Barnsley advance with Dean Bowditch scoring a consolation for the hosts.
The home side rallied at the start of the second half and Bowditch's goal gave them hope of getting something out of the tie but it was the slow start to the game that riled Robinson.
"I thought in the first half we were poor," he said. "We were as bad as we have been but the second half was more like us, tried to retain the ball and play the game right. It was a very split game, they were the better team in the first half and we were better in the second half."
MK Dons have not won in any competition since beating QPR 4-2 in round four of the FA Cup and Robinson admits being left with just the league to focus on could prove to be a blessing in disguise.
"Whilst we have had a good FA Cup run we've had a bit of a disappointing league campaign," he added. "Now, in some ways, to focus our minds on one thing might not be a bad thing."