The Gunners got through to the semi-finals of the competition with a 2-0 home win over Wigan Athletic on Tuesday night and are now the firm favourites for the title after West Ham knocked out Manchester United.
But Wenger insists he is taking nothing for granted as clubs such as the Hammers, Aston Villa, Birmingham and West Brom are still in with a chance.
"We have to accept there are no guarantees, even if we are in the semi-finals, that we will win the trophy. You have to fight in every single game to win.
"The supporters always want more, which is completely natural.
"You cannot say that [a first trophy] is not important, but we should also not make an obsession of that.
"We want to focus on the quality of our performances, and the rest will be the consequences of those performances.
"The major trophies are the Champions League and the [domestic] championship, but if we can win this as well, we will take it.
"We want to win trophies and be at the top, but you can only do as well as you can.
"At the moment, we are at the end of November and are in quite a good position in all of the competitions."