The Turkish manager backed his players to repeat upsets of the past on Wednesday evening but warned his players of the threat posed by Robin van Persie and Shinji Kagawa
Terim took inspiration from the likes of Besiktas, who beat United on their own turf in 2009 – albeit against a youthful starting XI.
The 59-year-old coach does regard Sir Alex Ferguson's team, however, as the most successful in Europe and warned his players of the threat posed by two of their attacking stars.
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"We can repeat that success. For me, Manchester United is the most successful club in Champions League football. Last year's failure doesn't change that.
"I was there at the Camp Nou as the Galatasaray coach when they'd beaten Bayern Munich and claimed the Champions League trophy.
"They have the likes of Robin van Persie and Shinji Kagawa who is a very special player in my opinion. We do not consider to use a man-to-man defence against their attacking weapons."
Terim admitted that Galatasaray would need to deliver an improved performance to stand a chance of avoiding defeat at the hands of the Red Devils, despite sitting top of the Turkish Super Lig table with an unbeaten record after four matches.
The former national team boss insisted, however, that the result would not be decisive in determining the outcome of the group stage.
"This year, we're the only Turkish club at the competition and thus, there's a huge pressure on us as a team," Terim said.
"I went on to become a successful manager thanks to my players' good performances before. Our performances so far this season are not enough to clinch victory at Old Trafford. We need to build on it and improve.
"I want my players to put everything on the field and win this game. The result of this clash will not be decisive for the group. It just will mean a good start, or a bad one."