The Saints exited the competition at the third qualifying round stage on Thursday evening after losing on penalties against the Belarusian side.
However, Millar has insisted that the wrong team progressed to the next round.
"We're a better team than Minsk - there is no doubt in my mind," he told PA.
"Over the two legs I thought we had done enough to get through but we never. We missed three penalties and that's it now. Football can be a cruel sport sometimes and it hurts.
"There are strong characters in that dressing room and the manager [Tommy Wright] is a strong character as well."
St Johnstone face Kilmarnock in the Scottish Premiership on Sunday.