Having restricted the Merseysiders to a solitary David Ngog goal almost a week ago in the first leg at Anfield with a resolute defensive display, the Romanian champions need to change their emphasis.
Thursday's game is being played at Steaua Bucharest's stadium as Urinea's 7,000 capacity ground does not meet UEFA standards but Levy still hopes to use home advantage.
"I believe at home we will try to attack more and with the support of our fans maybe we can surprise Liverpool," said Levy, whose side are in only their second successive season of European competition.
"This game is very important to us."
Midfielder Sorin Paraschiv was one of the players who provided the defensive screen at Anfield but he admits they cannot afford to be so negative this time around.
He pointed to their previous performances in the Champions League which, like Liverpool, they exited in December when they beat Sevilla - currently fourth in La Liga - at home and held Stuttgart and Rangers to 1-1 draws in Bucharest.
"I don't think we'll defend, not with the crowd behind us, pushing us on. We'll aim to do more," he said.
"At home we have played very well in Europe. We beat Sevilla so perhaps we can do the same against Liverpool, although I think Liverpool right now are stronger than Sevilla."
Fellow midfielder Sorin Frunza added: "At this level you cannot speak about strong or weak teams but Liverpool are a strong team and when you make a mistake they punish you."
Unirea will be without Argentinian defender Pablo Brandan as his booking in the first leg rules him out with suspension.