Both players arrived at San Siro during the January transfer window - Podolski on loan from Arsenal and Shaqiri on a permanent deal from Bayern Munich.
UEFA regulations state: "For all matches from the start of the round of 32, a club may register a maximum of three new eligible players for the remaining matches in the current competition."
However, the rules go on to say: "One player from the above quota of three who has been fielded in a UEFA club competition group stage match for another club in the current season may exceptionally be registered, provided that the player has not been fielded: a) in the same competition for another club; or b) for another club that is currently in the same competition."
That means only one of Podolski or Shaqiri were allowed to be selected, with the Germany international the unlucky man to miss out on a European berth.
Davide Santon, who arrived on loan from Newcastle United on Monday, has also been added, along with youngster George Puscas.
Pablo Daniel Osvaldo is among the players to lose their place in the squad, with Inter reportedly looking into cancelling the striker's loan from Southampton.
