Quins took some time to subdue the visitors, but once Zebre picked up two yellow cards in quick succession it was a case of damage limitation as the home side scored seven tries and collected 18 points from the boot of Nick Evans.
"We were imprecise and made mistakes but it was ultimately a job well done," O'Shea said. "We scored over 50 points in each of the two games against them. Before we first played them I read out their scores to our players and it showed that after 55 minutes of each game they had been in contention so they take some breaking down."
Zebre centres Daniel Halangahu and Gonzalo Garcia as well as flanker Filippo Ferrarini were yellow-carded, and O'Shea added: "When I stopped looking the penalty count was 24-4 in our favour.
"That's the fourth game in a row that sides have conceded over 20 penalties against us and it shows what teams are trying to do to stop us playing."
The bonus-point win ensured that Quins, who beat Zebre 57-14 when the teams met in Parma last week, only have to secure one point from their remaining two games to top Pool Three and hopefully secure a home draw in the quarter-finals.
"We want to be at home in the quarter-finals in April. People say that we are stuttering along but we've won 13 out of 16 in all competitions," O'Shea said.
"We are unbeaten in Europe, top of the Premiership and have won both our LV=Cup games."
Zebre lock Josh Sole was magnanimous in defeat, saying: "Full credit to Harlequins, their scrummage power was awesome and they taught us a huge lesson in the past couple of weeks."
- Sports & Recreation