The Gunners were seven points adrift of the Champions League spots last month following a 2-1 defeat at rivals Tottenham Hotspur, which left them with a slim of obtaining a place in Europe's elite competition next year.
However, Arsenal are now just two points behind Chelsea and Spurs with a game in hand on their North London nemeses, and Koscielny believes that they have responded well to the pressure.
"I think it is good to have a little pressure," Koscielny told Arsenal's official website. "Not a lot because then you can't play, you are afraid and you do nothing on the pitch. A little pressure is good to make sure you give your best for the team.
"We haven't won a trophy for a long time, and I think it's important to have this pressure for yourself, for the club, to give your best on the pitch.
"You need some luck, to have players who are in form as well. It is difficult but if everybody is ready to fight together and be focused then you can be successful."
Arsenal host Norwich City on Saturday.