The Londoners, Toulouse and Gloucester are all still in the mix for a quarter-finals place after the 'Quins superb backs against the wall display in their 31-24 victory in France.
"It has been a pretty tough run for the guys and we have come through it top of the Premiership table and, importantly with this evening in mind, playing for a place in the last eight of the Heineken Cup," said O'Shea.
"As a group we are getting used to playing massive games each week and this is part of our learning curve - every game has something massive riding on it and Saturday is yet another one of those.
"The victory in Toulouse was a seminal moment for the Club, but counts for nothing if it is not backed up on Saturday, and that will set us up for the last pool game next week in Galway.
"It is the time of the season when you have to compartmentalise competitions; Heineken Cup for two weeks, Anglo Welsh Cup for two weeks and then back to the Premiership with home games against London Irish and Worcester."
O'Shea admitted his 'Quins side will not under-estimate their visitors Gloucester when they arrive in the English capital.
"Gloucester represent a huge challenge to us, as they are developing one of the most talented squads in the country and play with a huge amount of width but also have a pack who can really mix it up," said O'Shea.
"We want to be in the mix as a group of coaches and players at the business end of competitions but that involves an understanding that you make things happen, things don't just happen just because you are at home or because you turn up.
"There is a work rate on the pitch which makes things happen, there is unseen work which makes the scores or keeps the defensive line intact. That is the work ethic we will need on Saturday. We aim to play with our usual tempo and physicality but it is all underpinned by a huge desire and work rate."