Szczesny was a late replacement for Artur Boruc for Poland's World Cup qualifier against England at Wembley.
And the 23-year-old produced an impressive performance despite his country's 2-0 defeat, a result that clinched England's place at next summer's finals in Brazil.
Szczesny was involved in a collision with England striker Danny Welbeck, which left the keeper nursing his arm.
"He just stood on my hand, but it was nothing serious," Szczesny said.
Meanwhile, the Gunners stopper is looking for the team to continue their positive start to the campaign when Premier League action returns this weekend.
Arsenal host Norwich on Saturday, with Arsene Wenger's men looking to consolidate their position at the top of the table.
"I hope we can keep going the way we have in the past few weeks and will give ourselves the best chance to challenge for a trophy," Szczesny added.