Arsenal blew the chance to move back to the top of the table on Monday when they drew 0-0 against rivals Chelsea at the Emirates Stadium.
The Gunners were five points clear at one point last month, but Liverpool are now top of the pile approaching the half way point.
Szczesny joined Arsenal in 2006 - a year after the Gunners won their last trophy.
He knows the last eight years have been hard for the club's fans and he is determined to make sure this is the year the supporters' agony ends.
"I'm very positive," said the Arsenal goalkeeper when asked to assess the team's chances of winning their first league title since 2004.
"We want to win trophies this time.
"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."
Arsenal take on West Ham at Upton Park on Boxing Day and they then face Newcastle, Aston Villa, Cardiff, Fulham and Southampton before the end of January.
Szczesny reckons the coming days may well decide who tops the table come May.
"This Christmas period is going to have a huge bearing on the season," the Pole said.
"The games are coming thick and fast. You know that teams will drop points.
"We've had a very tough run recently and now we've got a lot of games coming up and we want to take advantage of the fact that the big teams are playing against each other.
"Liverpool play Chelsea and Man City (on Boxing Day), so we want to collect our points and be right there at the top come the new year."
Lukas Podolski returned to the Arsenal bench against Chelsea following a four-month lay-off, but Arsenal manager Arsene Wenger is reluctant to start the Germany striker at Upton Park.
Laurent Koscielny could return, though, after sitting out the Chelsea game because of a cut to his knee.
Midfielder Mikel Arteta suffered swelling to his right ankle following two strong tackles against the Blues, but he is expected to be fit for the London derby.