AC Milan took the biggest price in European club football in 1989 and 1990, but no one has managed to retain the Champions League since the start in 1992.
“It would be very special to be the first team to retain this trophy,” said O’Shea.
“It is a major challenge for us but facing demands like that and responding to them is what this club is all about.
“If we are still in it after the group stages, when the competition really kicks in, we are in with a great chance.
“With the squad we have, we feel with a bit of luck at the right time, it is ours for the taking.”
O’Shea added on their Champions League clash against Danish side Aalborg on Tuesday: “The result Aalborg got at Celtic was an eye-opener for us.
“We saw how competitive and compact they were and we will need the right attitude to get the right result.
“We have a lot of experience of keeping the ball and quietening down a great atmosphere away from home in Europe and we will need it if we are going to get the result we want.”
