The Serie A team managed only one win from six games in their last campaign, showing they were well short of the benchmark in Europe's top club competition.
Garcia's team squeaked into this year's tournament courtesy of a last-gasp win over bitter rivals Lazio in May and will have a taste of what lies ahead when they take on heavyweights Real Madrid and Manchester City in the International Champions Cup in Melbourne over the coming days.
"We want to improve and get one round further at least," Garcia told reporters in Melbourne on Friday.
"I'm sure we have gained valuable experience last year and I'm sure it will be a valuable lesson."
Roma play Real Madrid at the Melbourne Cricket Ground on Saturday before a match against Manchester City at the same venue on Tuesday.
The Italians have pledged to be assertive in the transfer market and will be in close proximity to one of their targets in Melbourne in City striker Edin Dzeko.
Italian media reported Roma's sporting director Walter Sabatini flew to England in pursuit of the Bosnian but veteran forward Francesco Totti said he, personally, would keep a respectful distance in Melbourne.
"It's not down to me to convince him," he told reporters. "I'm sure that if he should come to AS Roma he can surely help us. He's a world class player and has a very good eye for goal."
(Editing by Sudipto Ganguly)
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