The north London club ended their nine-year wait for a trophy when they beat Hull City in the final back in May.
Now we just want to win more because now we’ve started to taste
The Gunners secured their first piece of silverware of the season when they beat Manchester City 3-0 in the Community Shield earlier this month.
And Koscielny is confident of more success this term.
“We won the FA Cup last season and I think that was very important for the players, the club and the fans,” Koscielny told Arsenal Player.
“We are under no pressure this season about winning a trophy. Now we just want to win more because now we’ve started to taste [what winning a trophy is like], and we want to have more.
“During August, the most important thing was to qualify for the Champions League. We did well [to achieve] this. The start of the season has been good, because we won the first game and got a good draw at Everton.
“You have a lot of games every three days with the Champions League and Premier League, and you have the Capital One Cup too. September to February is a marathon and we need to be fit and ready mentally.
“It’s very important to be ready for the fight and we just want to be happy, to give ourselves for the team and to win the game.”
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