O'Shea said: "Do not forget that we are only the second team in 16 years to win a European tie at Thomond Park - I could not be prouder of the boys.
"I always believed we had that sort of performance in us. This proves that we can deliver on the big occasion.
"It's from wins like this that we can move the club forward. But we have done nothing yet. We have won a semi-final and now we have a massive game against Stade Francais in three weeks time."
Quins 14-7 at the interval but produced a great defensive performance in the second period to become just the second side - after Leicester Tigers - to win a European tie against Munster in Limerick in the past 16 years.
O'Shea added: "We knew we would have to ride our luck at times. But when Chris (Robshaw) won the toss and opted to play into the wind, that showed the belief in the side and the type of rugby we want to play.
"Some of the hits we put in showed our commitment and we would not be cowards.
"Now we have a shot at silverware. and qualifying for next season's Heineken Cup.
"We created a lot of chances and we have to keep playing like that. If we do, we will only improve.
"Some of the talk during the week was that we would come over here, roll over and have our tummies tickled but that was never going to happen. I said to the players, 'Win your own individual battles and go minute by minute and see where it takes you.' They deserve to celebrate tonight."