They didn't. They lost a battle but that isn't the same as the empire losing to the Mameluks. I replied to someone else who asked a similar question here.

The gist of it is that Hulegu had about 150k men in the middle east but he traveled with his men to Mongolia to vote on who should be the next great Khan when Mongke Khan died without naming an heir. He left behind 10k men as a garrison. This is the force the Mameluks beat.

Civil war broke out in Mongolia when two of Mongke's brothers, Kublai and Arik Boke declared themselves great Khan and the various Mongol Khanates waged war against each other for a while and were too busy to deal with the Mameluks for the time being.