The Gunners have failed to win a piece of silverware since the 2005 FA Cup, with many of the current squad without a trophy to their name since joining the club - including the goalkeeper.
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"We want to win trophies this time. The time for reflection is when we’ve finished the season," he is as quoted as saying by the Daily Mirror.
"I'm very positive. The mood around the club is much better than it was at the start of the season. People maybe didn’t believe in this team as much as they do now.
"Our confidence is still quite high and we believe that we can go and do it this year. We’re looking forward to proving that.
"I don’t think the belief within the group was ever missing. This year we’ve just been more consistent. That’s made all the difference. We have to keep it going.
"Winning the first trophy is so important. We’ve been missing a trophy for quite a few years and that’s not good enough for such a big club.
"But we enjoy the pressure because we believe that we can be the team that will deliver for the fans and for the club."
A 1-1 draw with Everton on December 8 prevented Arsenal from going seven points clear at the top of the table, with a 6-3 humbling by Manchester City and a 0-0 stalemate with Chelsea seeing Liverpool overtake them on goal difference.
Next up for Arsenal in a London derby away at West Ham on Boxing Day before a trip to Newcastle and the visit of Cardiff follows over the next six days - and Szczesny feels performing during this busy schedule is crucial.
"We’re in the middle of a very tough season and we have to look ahead rather than back at what has already happened. We’re in a strong position. This Christmas period is going to have a huge bearing on the season.
"We want to take advantage of the fact that the big teams are playing against each other so we want to collect our points and be right there at the top come the New Year.
"After losing like we did at Manchester City, it’s massive for us to play another of the big teams straight away in Chelsea and show we can match them. It’s so important for our confidence.
"Two or three years ago we’d have lost the Chelsea game. Sometimes if you can’t win it, you have to settle for a clean sheet and a point."