Adem Ljajic's early goal in the Serie A clash was cancelled out by Paolo De Ceglie and the game looked to be heading for a draw, however, the Bosnian midfielder had the last word, curling an 88th-minute free-kick into the top-right corner.
Garcia reserved special praise for the goalscorers and was pleased with how his Giallorossi charges overcome potentially tricky opposition.
"We played well with a very good first half that had quality possession," Garcia told Sky Sport. "It's always difficult to come to Parma and I really like their coach Roberto Donadoni, even though we saw a more defensive Parma tonight.
"I am very happy for Adem Ljajic, and I knew at the break we'd probably struggle on set plays. Other than those, we weren't really allowing any chances.
"How did we resolve the situation? Gave Pjanic the ball and watched him score a genius free kick."
Roma have been struck by a number of injuries in recent weeks, testing the depth in Garcia's squad, but his players have responded in style as they are only behind the three-time defending champions Juventus in the table on goal difference.
"We played five games this season and never had the same defence twice," the French coach added.
"All of them are important and with this series of injuries, which thankfully ground to a halt today, I have at least been shown that I have many great men to rely on."