Kevin Strootman put away an Adam Ljajic cutback in the 90th minute as Roma secured their fourth straight league draw.
Davide Brivio had given Atalanta a 51st-minute lead with a long-range free-kick.
Garcia, whose undefeated team sit three points behind league leaders Juventus, praised his side for pushing until the end.
"I was very satisfied with the performance I was watching from the bench because my team was attacking all the spaces on the pitch," he said.
"We spent a lot of time in our opponents' area and my players showed their enthusiasm and ability.
"It's very satisfying for a manager to see his players playing like this, especially when the score is 1-0 to the opposing team. I believe Roma will have a very positive future."
Roma midfielder Daniele De Rossi was substituted after 57 minutes – replaced by Ljajic – after receiving an early knock.
Garcia said it was a precautionary move as well as a tactical one, wanting to give Roma more drive in midfield.
"De Rossi plays his role in an extraordinary way and no-one can play in that role better than him," he said.
"Daniele's problem was that at the beginning of the match he was hit where he already had the injury that prevented him from playing the two matches with the Italian national team.
"After that blow he wasn't at 100 per cent in terms of his conditioning and I decided to substitute him because next week we have to play a very important match (against Fiorentina) and also because we need a forward who's able to support Gervinho and to penetrate the opponent's area.
"That's why I decided to substitute Daniele De Rossi."
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