Garcia, who was appointed in place of the sacked Sylvinho on Monday, could only watch as his new side was held 0-0 at home by modest Dijon, the league's bottom team.
It stretched Lyon's winless run in the league to eight games and left the side 16th in the 20-team division, 14 points behind leaders PSG after 10 games.
The 55-year-old Garcia was not given the friendliest welcome as Lyon fans remembered his tenure in charge of bitter rivals Marseille and Saint-Etienne. Garcia left Marseille after three seasons in May.
Also Saturday, Nantes, Angers and Lille all lost, leaving PSG with a five-point lead following its 4-1 win at nine-man Nice on Friday.
Second-place Nantes lost 1-0 at struggling Metz, ending the visitors' three-game winning run, and Angers lost 1-0 to visiting Brest, allowing Reims move third with a 1-0 win at home over Montpellier.
Toulouse defeated Lille 2-1, and Nimes drew with Amiens 1-1.