Garcia's side remain in the running for the Serie A title and have already secured a top-three finish, having won their last seven top-flight matches.
In Garcia's debut season, such a performance represents progression for Roma - and the Frenchman is eager to continue building for Europe while also fighting for the title, even though they sit five points behind leaders Juventus, who also have a game in hand.
However, he also called for patience from the Roma faithful and warned they will not be able to compete with the continent's premier clubs straight away.
"After a season like the one we're having, every coach would like to keep the squad together and strengthen it with further signings," he said.
"The only thing I hope that we don't do, and this happened to me at (former club) Lille, is go into the Champions League just to make up the numbers. We're Roma and hopefully we'll build a team capable of getting through the group stage.
"There are lots of great sides in Europe at the moment but, as they say, Rome wasn't built in a day.
"We won't know until next season how competitive we can be in Europe. At the moment we're doing lots of things well: we play at a high tempo, we close down well and I'm very happy with the attitude I've seen in these games."
