The Turkish giants won the Super Lig last season, and have been subsequently rewarded with a place in Group H, which consists of Manchester United, Braga and CFR Cluj.
They return to the Champions League after a four-year absence and Terim is determined to make it a successful comeback.
"Let this be a good campaign for the entire Galatasaray community," he told reporters.
"Europe missed Turkey, and so too Galatasaray. I hope it will be a long European adventure."Reflecting on Galatasaray's opponents in the pool, Terim is aware of the threat that Manchester United pose, but hopes to cause a major upset in this year's competition.
"Manchester United are a team who everybody must respect. Many years ago, Galatasaray enjoyed victory over Manchester United. I hope we can repeat that."
The 58-year-old was also complimentary towards his Portuguese opponents, but expressed how he will respect every side and maintain a high level of preparation during their European run in order to avert complacency.
"Braga have done well in recent years," he added. "Football is a serious business and we shouldn’t underestimate anybody.
"This will be our key principle. We set our target of qualifying from the group a long time ago."
"Matches are won on the pitch. Therefore we’ll prepare in the best way we can to achieve this. I was going to say the same regardless of the teams we were paired with.
"I don’t rely on luck. I never have. If you don’t put in enough effort, you may finish fourth in this group. Without thinking of the power of our opponents, we must our own game."
Cimbom begin their Champions League conquest away to Manchester United on September 19.