Leonardo Bonucci's superb volley earned defending Serie A champions Juve all three points in the eagerly anticipated top-of-the-table clash in Turin.
However, it was official Rocchi who took most of the headlines due to a host of debatable decisions, notably the awarding of two penalties for Juve.
The first of the spot-kicks was given for handball against Maicon after Rocchi originally appeared to award a free-kick, while the second was judged a foul by Miralem Pjanic on Paul Pogba, with what minimal contact there was perhaps occurring just outside the area.
Those penalties came either side of a Francesco Totti spot-kick and Juan Iturbe's effort as the teams were level at 2-2 at half-time.
The match also ended with a fracas that saw Juve's Alvara Morata and Roma's Kostas Manolas sent off.
Garcia, who was himself sent to the stands, criticised Rocchi's performance and suggested that more technology should be used to aid referees.
"It's a shame that the penalty boxes are 19 yards here," he said in reference to Pjanic's challenge on Pogba. "But I'm pleased with my players for the character they showed.
"Things got a bit too tense out there but normally you have a ref who knows how to deal with those things.
"Perhaps it's time to help the referees work out when it's a goal or a penalty.
"This is the 21st Century, a foul is outside or it's inside [the area], simple. You can have replays at pitchside and it would help."
Garcia did concede, though, that Roma did not play to their full potential.
"Lots of things went on out there today but we're partly to blame ourselves as well," he added. "We had two great chances to score and we were beaten by three set-pieces.
"We did enough to win. If I think of the chances Pjanic and Gervinho had, we could have done better there."
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