The official reversed a decision to award Sassuolo a penalty in the first half of Roma's 2-0 win but the Frenchman believes it was correct
Garcia's men claimed all three points at the relegation-threatened side thanks to a 16th-minute strike from Mattia Destro and substitute Michel Bastos' injury-time effort.
But the game was marred by Rizzoli's controversial decision, in which the referee, who will feature at the World Cup later this year, initially pointed to the spot in the 36th minute after Roma defender Mehdi Benatia appeared to have fouled forward Nicola Sansone.
However, after angry protests and consulting with his assistants, Rizzoli overturned the call, instead signalling for a drop-ball.
And Garcia believes that the official made the correct move to change his mind.
"It's never easy to win on the road," he said.
"I liked our play until the incident between Benatia and Sansone where Rizzoli made the right call."
Garcia remains hopeful that the capital club, who approached the weekend 14 points behind Serie A leaders Juventus, can win a first Scudetto since 2000-01.
Juve face a tough test at third-place Napoli on Sunday and, despite needing a significant points swing to finish top, Garcia is not giving up.
"There's a big gap with Juve," Garcia added.
"But we'll keep going while it's still mathematically possible."