After conceding three goals during the opening 45 minutes in Denver, Roma rallied in the second half with a stunning long-range strike from Miralem Pjanic and Francesco Totti's penalty.
But the Serie A outfit could not avoid defeat in their International Champions Cup fixture, after overcoming Liverpool 1-0 on Wednesday in a non-related friendly.
Speaking to reporters post-game at the Sports Authority Field, Garcia lamented his team's efficiency up front.
"It was a shame to go into the break 3-0 down. We need to be sharper, because if 2-0 down at half-time we could well have won," he said.
"The result was excessive but at the end of the day they won and deserved it.
"The difference was in their efficiency, as Manchester United had 50 per cent more shots on target."
Roma's starting XI featured eight players aged 23 or younger, with Arturo Calabresi (18), Alessio Romagnoli (19), Leandro Parades (20), Salih Ucan (20), Juan Iturbe (21), Mattia Destro (23), Alessandro Florenzi (23) and Lukasz Skorupski (23).
"There were many youngsters today who had never even played in Serie A, so it was natural to feel a little nervousness against United," Garcia added.
Garcia reserved praise for Bosnia-Herzegovina international Pjanic, who sensationally scored from inside his own half.
"Pjanic's goal was fantastic and will go all round the world. I can say the training session with the [NFL's Denver] Broncos did him good," the Frenchman said.
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