Manuel Pellegrini opted to bring Costel Pantilimon into his starting XI after the England international made a string of high-profile errors, notably against Chelsea and Bayern Munich.
But Szczesny, who was dropped himself by the Gunners last season before bouncing back and being rewarded with a new contract, expects the 26-year-old to come back stronger from the experience.
"I personally rate him as one of the best, if not the best, goalkeepers in the world," the Pole told reporters. "Age has this thing where you are not as consistent as an older goalkeeper [is].
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"Forget the last couple of weeks, where it has been very difficult for him and he has been dropped. I suppose everybody has got to go through that.
"Over the last couple of years, he was the most consistent and one of the best – it is hard to say the best – goalkeepers in the world and I am sure that he will prove that to people even though he has had some difficult times.
"You have got time to sort things out," the Arsenal keeper added. "A lot of aspects come into the game of the top goalkeepers.
"You can become too professional, if you like, you get too serious about things and try too much and that can backfire so it is very important to relax and maybe have a bit of time away from the pressure, getting the right mindset and it seems to be working.
"I definitely hope Joe will do the same and, if he comes back stronger than he was before, then it is scary to think how good he is going to be."