Francesco Totti's 58th-minute goal handed Roma a 1-0 victory in the International Champions Cup at the Cotton Bowl in Texas on Tuesday.
Garcia, while praising the triumph, was keen for Roma not to get ahead of themselves and insisted that his team still have much work to do to get to the level of the European champions.
"Real Madrid are ahead of us," Garcia said.
"We won a friendly match. Of course it is always better to win. We are ambitious and it is nice to dream, because if you do not dream then you get bored.
"In the Champions League we are thinking of progressing from the group stage. Our priority is the league and we want to finish on top.
"There are so many good teams but we want to finish out ahead.
"What do Roma lack for the Champions League right now? It's hard to say we still have much to do. However, we are on the right track."
Roma finished second in Italy's top flight last season and veteran captain Totti has urged the team to fight to go one better this time around.
"Is the objective the Scudetto? Yes, we want to do better than last season. This club must fight for the Scudetto," he added.