The Nerazzurri were clear favourites to collect an opening three points in a Group B match against the unfancied Turkish side, who are only in the tournament because compatriots Fenerbahce had been kicked out due to match-fixing allegations.
Despite dominating the match, Gasperini's men were unable to find a breakthrough and were punished by a 75th minute strike by Ondrej Celustka.
Speaking post-match, the under-pressure Inter coach insists his side will bounce back from the defeat.
"Paradoxically, this defeat may lead to a reaction," he told Sky Sport Italia. "The season has just begun and we will find the strength to react.
"A lot has been said about tactics, it is too simplistic to talk about football that way. This game was better [than the one against Palermo] in some aspects, but the result is what matters, and it was a bad one."
Demanding Inter president Massimo Moratti is believed to be running out of patience for the 53-year-old after losing all three of Inter's opening games to the season which included defeats to AC Milan in the Italian Supercoppa and Palermo in the Serie A.
But Gasperini insists he is under no pressure from Moratti.
He added: "This story about President Moratti pressuring me is not true.
"He has always been very supportive towards me. We discuss things, but do not make it look as if it is something that it is not."
Inter travel to CSKA Moscow next on 27 September.