Roma played a friendly in Indonesia on Friday, defeating the Indonesian Under-23 team 3-1 at their base in Trigoria with Garcia sending out three different line-ups for 30 minutes each.
But Cole, who signed from Chelsea on a free transfer on July 7, did enough on debut to earn some praise from Garcia.
"I liked the attitude of the new players like Cole and [Salih] Ucan," Garcia was quoted as saying by the Daily Mail.
"They stepped on to the field with confidence."
Former England international Cole joined Roma after eight seasons with Chelsea, where he won a Premier League title, four FA Cups, the UEFA Champions League and the UEFA Europa League.
The 33-year-old has a contract with the Italian capital club for the next two seasons.
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