Quins made sure that they finished Pool 3 with six wins from six matches on Friday night as Biarritz suffered a rare defeat in France.
"It was a mature performance and we are delighted with the attitude of the players," O'Shea told Sky Sports News.
"There was a lot of experience out there of playing together and in tough conditions but it was one of those nights when you had to roll the sleeves up and show as a group what it means to play for each other. We had to grind it out."
Quins had made sure of a home quarter-final in the competition before their triumph in France.