While a lot needed to be done, the state government was trying to spruce up the system, Qureshi - who is holding additional charge of the state - told reporters in what was his last official engagement with the media.
"Yahan par to aap poori duniya ki (police) force laga dein to bhi balatkaar jaisi afsosnaak ghatnayein nahin ruk sakti" (Even if you put the entire world's police force on duty here, you won't be able to prevent unfortunate incidents like rape), he said.
In the same breath, Qureshi said if only gods came down from heaven, will there be an end to such crimes.
The governor's statement came in the wake of several incidents of rape and murder of women in Uttar Pradesh in the recent days.
With this statement, the governor joins a list of politicians who have been giving uncharitable remarks on rapes in the state.
Former chief minister Mulayam Singh Yadav earlier said rapes were "minor mistakes committed by youngsters" and that laws sending rapists to the gallows must be quashed.
After last week's rape and murder in Lucknow that caused considerable outrage, the Samajwadi Party chief attributed growing crimes against women to the rising population.
His brother and PWD Minister Shivpal Singh Yadav later endorsed his views.
Asked about the failing law and order after the Badaun incident, where two minor girls were gang-raped and then hung from a tree, Chief Minister Akhilesh Yadav had snapped at a woman reporter: "You are safe... so why rake up the question?"