Roma were hoping to reach Serie A's mid-season break just a point behind leaders Juventus.
However, Milan left Stadio Olimpico with a point despite playing a good chunk of the second half with 10 men after Pablo Armero was sent off in the 71st minute.
Head coach Garcia believes Roma should have had the opportunity to move ahead before half-time, though, when an apparent handball by Nigel de Jong in the penalty area went unpunished by the referee and his two assistants in the Milan half.
"It should be said that there was a pretty obvious handball in the area," he told Sky Sport Italia.
"I've said this before but if the goal-line officials don't take responsibility for things there's no point having them."
Roma were well below their best in front of their home fans, although Diego Lopez twice made smart saves from the impressive Gervinho - the latter coming deep into second-half stoppage time.
"We could have done better ourselves," Garcia added. "Milan defended well with five in midfield and left little space between the lines.
"Two points dropped? Yes, we had the chances to score but should have tested the keeper more.
"We lacked a bit of creativity. We wanted to play more down the channel where De Jong was, that's what we'd planned."
Roma are now not back in action until January 6 when they travel to Udinese, and Garcia is looking forward to recharging his and the Roma players' batteries.
"All the clubs welcome this break. Footballers aren't machines, they can't go 10 months non-stop without resting."