Fabianski conceded the first but was later substituted after a nasty collision with defender Thomas Vermaelen.
"I think I am fine, it's just a really deep cut," he told Arsenal Player. "It was really unlucky but hopefully all the ligaments in my knee should be OK. Hopefully nothing will come out tomorrow or in the next couple of days.
"I can only talk about the time I was on pitch because afterwards I didn't see anything.
"You could see that Olympiacos were really up for it and they were pushing hard. The first goal we conceded was a bit unlucky because it went off our defender.
"We could have maybe come back in a different way but unfortunately we didn't and that's how it finished."