"I announce my resignation from the post as it is prerogative of the winning party to have its nominee in Punjab," Mahmood said.
The Pakistan People's Party lost the election because it failed to address issues like a crippling energy crisis, he said.
"The PPP concentrated on strengthening democracy after coming to power but ignored the issue of governance," he said.
If the new government did not deliver, it too would meet the same fate, he said.
Mahmood's son bagged the only parliamentary seat won by the PPP in Punjab, the country's most populous province.