The Gunners drew 0-0 at champions Leicester on Saturday and remain winless after the opening two Premier League games.
Travelling fans again turned on Arsene Wenger and urged him to spend as the toothless visitors struggled to create clear chances.
But defender Koscielny insisted the Gunners, runners-up to Leicester last season, will battle for the Premier League crown as they hunt their first title since 2004.
“Always. We are Arsenal – we fight for the title. Every game we play we want to win the game,” he said.
“This season will be very difficult because of the top clubs spending a lot of money on transfers, it’s unbelievable. But sometimes the collective can be better than individual players. So we want to keep our philosophy and play football.”
The 30-year-old made his first appearance of the season at the King Power Stadium after returning to the Gunners late after helping France to the final of Euro 2016.
Koscielny was part of the national side which lost 1-0 to Portugal and was not fit to play in last week’s 4-3 defeat to Liverpool but said it is natural for players to need more time to recover.
“You could see last week we lost Aaron Ramsey with an injury and now he’s out for one month,” Koscielny told arsenal.com. “When we have a summer tournament it’s the same for every other team, not just for Arsenal. I’m sure every other team is the same.
“The players come back later and need more time to be fit, to be ready for the game. Last week (we didn’t play) because we weren’t fit and it was important to have one more week for training to be fit this week, and you can see, no one got injured.”