And with a Heineken Cup quarter-final and a league title to play for Marshall insists he and his teammates will not be taking their Italian opposition lightly, especially after they ran them so close in the reverse fixture back in November.
That day Ulster were more than fortunate to escape with a 27-25 win and Marshall wants no more repeats of that close scare this time around.
"In years gone by, maybe we were the underdogs. We have aspirations to be one of the top teams in European rugby so there can be no off weeks," he said.
"The Ospreys was a tough came to come back into. In the first half, we didn't secure enough ball. It was a disappointing result and performance.
"Perhaps we got a bit ahead of ourselves and Ospreys caught us cold.
"Mark [Anscombe] was saying that, as we are setting the pace this year, teams will be coming for us."
The Ulstermen's only previous defeat to an Italian opponent in a competitive match was 12-23 at home to Treviso in October 2011.
And Mark Anscombe's troops have been boosted by the return of a number of key players ahead of the clash.
They welcome back Ireland forwards Declan Fitzpatrick, Iain Henderson and Chris Henry while backs Paddy Jackson, Darren Cave and Chris Cochrane are the other players coming into the team, while there are a further two positional switches.
Zebre meanwhile are still searching for their first win of the season, although they have led in six of their 14 RaboDirect PRO12 games this season so far.
And they welcome back Italian internationals Gonzalo Garcia and Paolo Buso while Italy U20 star David Odiete comes back onto the bench.
Last week's defeat to Glasgow Warriors marked the first appearance of the season for Marco Bortolami after an ongoing shoulder injury and the legendary second-row is hoping that there is much more to come from him.
"It 's nice to get back into the action on the field, to have a good time and get back to playing proper rugby and leave the field satisfied," he said.
"I'll have to put minutes on my legs to return to 100%, though the road is the right one. I will try to contribute for the rest of the season, we have to work because the victory is not far away but it never happens by chance: we must roll up our sleeves and work hard."
At Ravenhill , 7.05pm. Live on BBC Sport NI
Referee: Neil Paterson (SRU, 47th competition game)
Assistant Referees: Paul Haycock, Barry O'Keefe (both IRFU)
Citing Commissioner: John West (IRFU)
TMO: Peter Ferguson (IRFU)