"One more result would be good because we are not losing our heads and talking about getting to the knock-out stages or anything like that.
"We know we have suffered a bit up front in the past and the club has made a real effort in bringing in some new players to try and make us more competitive in the forwards.
"We now have a couple of South African-born locks, Marco Wentzel and Gerhard Klerck, and Klerck will also add considerable experience as he has played Test rugby for the USA Eagles.
"However, we have also been introducing some young players and the way they have performed has been a real bonus for us."
Benetton kick-off their Pool 2 campaign with a home game against Leinster on Saturday in front of the Sky Italia cameras, with Green hoping that his side can hit top gear against Reggie Corrigan's star-studded team.
"It is a great game for us to start with," he said. "I am happy it is a home match and also that we expect a lot of their supporters to make the trip, which is good for the club and good for rugby in the area.
"Leinster have many fine players, some of them world-class, but we always want to try to compete against the best - and Leinster are certainly one of the best in Europe."
Troncon, Benetton's international scrum half and captain, said: "The Heineken Cup has become a grand spectacle thanks to the high level of its participating clubs and leading players from all over the world.
"The Heineken Cup is an event that has found its own identity within the international rugby scene and that has its own solid financial base and large spectator support.
"Within the big picture I am sure that the Italian clubs can, and will, find their space and glory within this competition.
"Benetton Treviso has always been proud to be included in this competition and, as always, will be trying very hard to reach the quarter-finals."