Lofton played for the Falcons for four seasons before the club decided not to renew his contract after the 2011 campaign.
The 27-year-old then joined their NFC South rivals the Saints and comes up against Mike Smith's side twice a year.
Lofton told SiriusXM NFL Radio: "You never get over the team that let you go. I always want to beat them. I never want to lose to them."
The Saints face the Falcons on the opening day of the 2014 season in September.