The Aviva Premiership club currently head Pool Three following successive victories over Biarritz and Connacht, and Zebre, on paper at least, should offer little threat to the Londoners, either in Italy or when the teams meet at Twickenham Stoop on Saturday week.
Quins, though, saw their hopes of reaching last season's knockout phase wrecked by a 9-8 loss against Connacht in Galway, and wing Tom Williams said: "We underachieved in the Heineken Cup last season. Connacht did brilliantly to beat us in the final pool game, and that cost us, so we know we cannot afford to take any side lightly."
He added: "Zebre have only played a few games together. They've played twice in the Heineken Cup and then they have had their league fixtures in the RaboDirect PRO12, so we've done as much research as we can.
"We are doing well in all the competitions - we are top of the Premiership and looking good in the Heineken Cup - but it is a sign of how far we have come and developed as a team that we are still not satisfied."