Munster led 21-6 at halftime, but the Stormers' scrum took control to score 21 unanswered points in the second half.
That loss left the South African side as the only unbeaten side in the United Rugby Championship after six rounds.
Munster is third, one point behind Cardiff, who have an extra bonus point.
However, attention in Europe turns to the Champions Cup at the weekend, where Munster travels to Bath for its opening game, followed by Gloucester and Ospreys.
McMillan said the side will have to absorb lessons from the loss quickly.
"The positive thing is that our set-piece malfunctioned at times, we were ill-disciplined, yet we still gave ourselves a chance to win the game, and for all the lack of possession, territory and discipline, it wasn't that far off.
"We know what we're capable of when we play somewhere near our best; we just need to do it more often for longer.
"The games that we have ahead of us aren't going to give us the luxury of bumbling our way through and hoping that we come out on the right side of the scoreboard.
"We'll be honest in our review, as we always are, and we'll need to find some quick improvements because teams would have seen opportunities and chinks in the armour, and they'll come hard at us in those areas."
The disappointment evident in the Munster dressing room after the defeat was a positive sign of the care the players felt, and that would be important in preparing for Bath's threat.
"We know how good they are so we need to get better."
