The Serie A club - who were hit by the surprise resignation of long-serving honorary president Massimo Moratti earlier in the day - had won both qualifiers and their Group F fixtures with Qarabag and Dnipro going into the clash at San Siro.
But while Inter have still not conceded a Europa League goal this term, Walter Mazzarri's side could not break down a stoic Saint-Etienne team, who have now drawn all three of their group games.
A Zdravko Kuzmanovic strike well saved by Stephane Ruffier was as close as Inter came in a game of few chances as Mazzarri's men saw their lead at the top of the pool cut by a point to three after Qarabag's 1-0 win in Kiev.
Saint-Etienne, meanwhile, slip to third ahead of the return fixture at the Stade Geoffroy-Guichard on November 6.
Featuring against one of his former clubs, Inter skipper Fredy Guarin had the first effort at goal but blazed his strike over the crossbar from outside the area two minutes in.
Mauro Icardi was next to go close but he too failed to find the target when played in by Yann M'Vila.
Winger Ibrahima Mbaye came close to engineering an opening when he surged down the right but still the visitors stood firm amid Inter's domination of possession.
Florentin Pogba's free-kick found the Inter wall as Saint-Etienne made a rare foray forward and Kevin Theophile-Catherine almost gave Christophe Galtier's side a shock lead when he headed wide from the ensuing corner.
The visitors grew into the game before the break and almost had a half-time lead when Franck Tabanou let fly from a free-kick - Juan Pablo Carrizo required to tip the effort over.
Romain Hamouma saw appeals for a penalty waved away after going down under pressure from Mbaye early in the second half before Inter were dealt a blow as M'Vila limped off to be replaced by Hernanes.
While forced upon Mazzarri, the change seemed to inject some energy into Inter's second-half showing as the home side continued to dominate possession without really threatening Ruffier.
Ruffier was called on to tip Kuzmanovic's shot wide shortly after the hour while Theophile-Catherine blazed over when played in down the right 16 minutes from time.
However, neither side were able to break the deadlock as Inter extended their unbeaten run at home in Europe to nine matches but missed the chance to fully bolster their hopes of progression.