Efe Sodje's injury-time equaliser earned the Shakers a point after Reuben Reid's 83rd-minute penalty had put the Millers on course for victory.
Robins, assistant to Bury manager Alan Knill during the latter's spell in charge at Rotherham, said: "On the overall balance of chances, it was a fair result.
"But we're disappointed to have given a goal away on the last set-play of the game."
Robins had few doubts Reid would convert his spot kick for his sixth goal in the last five games.
He added: "I couldn't watch it. I turned my back, but he normally sticks them away well. Reuben Reid is a confident lad, so I didn't have too many worries."