The Gunners had to rely on a Robin van Persie wonder-strike in order to emerge victorious from the weekend clash at Emirates Stadium, which marked Arsenal's 125th anniversary as a club.
But Szczesny, who did manage to keep a clean sheet, insists that he is happy with the 1-0 victory despite it not being the most thrilling of matches.
"We said in the dressing room that it is good to win ugly every now and then," Szczesny told the club's official website.
"We did not create a lot of chances and missed a couple in the first half. But we stuck together and got the all-important winning goal.
"It is vital to win these kinds of games - especially in December when there are a lot of matches and it is easy to drop points."
Since their stumbling start to the season, Arsenal have since collected 22 points from their last possible 24, and Szczesny believes that they can push this momentum through to the Manchester City game next weekend.
"It is very important that we keep going now," said Szczesny. "We believe that we can win every game.
"We have a massive game against Manchester City coming up. They will be favourites this time but we are confident we can go there and get the three points.
"It is probably the toughest game of the season but people were saying that last year and we won 3-0. We hope to repeat the performance and hopefully the result as well."
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