Tierney sparked their comeback with an equaliser for 2-2 before Pierre-Emerick Abameyang headed home the winner.
"We all make mistakes all the time – sometimes they get punished and sometimes they don't, but in European competition they are going to [get punished] and they did," said Tierney.
“We bounced back the best way we possibly could and I think it is a good step for us to show we can face adversity, come back and go through.
“We never seem to do it the easy way. But credit to the boys we had some tough moments out there and some setbacks but to bounce back, score and go through to the next round, is all that matters.
“We are taking it game by game. We are not looking too far ahead, we have a big game on Sunday [against Leicester] as well. The games are coming fast right now so we can only look at one game at at time."
Arsenal have drawn Olympiakos in the round of 16.