David Ngog's 81st minute winner ensured Rafael Benitez's side take a slender lead to Bucharest for the return fixture at the Steaua Stadium next week, having been frustrated for long periods by Ronny Levy's side.
Bur despite the defeat, Levy said he believed his charges - who defeated Rangers 4-1 at Ibrox and beat Sevilla at home earlier this season - have more than a fighting chance of inflicting more misery on the Reds.
"We are a bit disappointed because the only time we lost concentration they scored," he said in The Sun.
"But this is still a good result to take back to Bucharest. It is an interesting situation and we still have a good chance."
Urziceni chairman Mihai Stoica echoed the thoughts of his manager, although midfielder Sorin Paraschiv could not hide his disappointment that Unirea could hang on for the draw.
"We are disappointed, we put up a fight. Very, very sad tonight," said Paraschiv.
Stoica added: "Tickets will be almost for free at home. It's just half-time, we can make home ground count. Gerrard is the most complete player in the world."
With thanks to Emanuel Rosu.
