The Serie A side were toothless against their French opponents at San Siro as their winning start to their UEFA Europa League campaign came to an end.
While dominating possessions for large periods, Group F leaders Inter were unable to break down the visitors and subsequently missed the chance to bolster their hopes of progression.
Mazzarri refused to comment on the surprise resignation of club icon Massimo Moratti as honorary president earlier on Thursday, amid reports the former president wanted Mazzarri sacked.
Instead, the ex-Napoli boss suggested the current situation was a drastic one, with Inter boasting just one win from their last five games in all competitions.
"We are in an emergency situation and playing every three days meant we weren't as sharp as usual," Mazzarri told Sport Mediaset.
"Today we had to change a great deal and considering the situation I think it was a good performance. The important thing was to continue picking up points.
"We are doing well in Europe even if of course we like to win every game. We had six youngsters on the field against Napoli on Sunday and put in a great performance.
"Of course I'd love champagne football but I don't see many doing that nowadays. Saint-Etienne are a team to be respected."
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