After departing his post as Italy head coach following their disappointing World Cup group-stage exit, Prandelli took over from compatriot Roberto Mancini, tasked with regaining the Turkish Super Lig title from fierce rivals Fenerbahce.
Prandelli will also be keen to prove his credentials in Europe, although Galatasaray have been dealt a tough draw, with Arsenal and 2012-13 runners-up Borussia Dortmund also placed in Group D.
A strong start to the group phase is therefore essential for Galatasaray, who reached the second round last season before being knocked out by Chelsea, and Prandelli wants the vociferous home faithful to add their usual fervent support on Tuesday.
"We might fall behind during the game," he said. "Our fans should always be backing us as we are stronger with them.
"We'll try to get three points with the help of our fans."
Belgian champions Anderlecht have been touted as the outsiders of the group, but Prandelli is refusing to take Besnik Hasi's men lightly.
"Let's not call Anderlecht the weakest team in the group," he said. "Let's say the youngest.
"Just because they have played more matches than us [in their domestic league], we won't have any fear of them.
"We'll play against an organised, very young and interesting team. They will be ambitious to impress. Therefore we need to be careful."
The visitors are seven games into the Belgian Pro League season and sit top of the table, still unbeaten, while Galatasaray have taken four points from two Turkish Super Lig matches to also occupy the summit.
