Having lost 2-0 to St Pauli on Friday night, the Edinburgh outfit were beaten 4-2 by another Bundesliga 2 side.
Ruben Palazuelos put the Scots ahead after just five minutes when he headed home but Adulkadir Ozgen levelled for the hosts 20 minutes later.
Benjamin Auer gave Aachen the lead shortly before half time when he rammed home after Hearts failed to clear a corner.
Eggert Jonsson restored hope for the visitors 11 minutes after the interval when he fired home the equaliser after a well-worked move.
However, it took Aachen little more than 60 seconds to restore their advantage as Thorsten Burkhardt headed in for the hosts.
Herve Oussale secured the victory for Aachen with 15 minutes to go when he raced clear to shoot past substitute keeper Jamie MacDonald.