Tom Williams, the player at the centre of 2009 bloodgate scandal involving Newcastle boss Dean Richards, opened the scoring before two tries from Sam Smith and one from Danny Care helped Quins to a 35-9 victory on Sunday at Kingston Park.
"We started slowly, but got into it and the score just after half time took the crowd out of it and deflated them," O'Shea told the press.
"We're more than happy with the win, but what excites me there is so much more within this group.
"We set ourselves a goal to get back in the fight and we're now back in the fight. We face a tough six days and face Racing Metro away, but we'll work on it and we'll be ready."
Quins travel to Racing Metro in the Heineken Cup on Saturday.