The Gunners are set to end an eighth straight campaign empty-handed, with silverware having passed them by for another year.
They are, however, focused on a bid to secure a top-four finish and the construction of a platform on which to build next term.
Koscielny believes success will come and claims to have no complaints at working under the mounting weight of expectation at Emirates Stadium.
The French defender told Arsenal Player: "I think it is good to have a little pressure.
"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's difficult, but if everybody is ready to fight together and be focused then you can be successful."