Domenico Berardi's 94th-minute goal ensured the league leaders were held to a second draw in as many matches, although they remain unbeaten in Serie A this season.
Roma took the lead in the 19th minute at the Stadio Olimpico after Alessandro Longhi turned the ball into his own net following an effort from Alessandro Florenzi.
Garcia's men missed plenty of chances to add a second and were punished when Berardi found the net with full-time looming.
The Frenchman admitted his side should have killed the game off, but refused to panic given they remain top of the table.
"All my players were angry at the end," he told the club's official website. "We’re disappointed, which is normal. It’s tough to swallow when you’re leading 1-0 and give up a last-second equaliser.
"We missed a lot of chances; when you don’t score that second goal then anything can happen. When you’re on the field and 1-0 up you can never relax.
"But off the field we’re still in first place and we feel calmer. We played a good game in the second half, better than we did in the first. If we play well we’ll manage to win more games."
Garcia also congratulated Sassuolo, who picked up their 10th point of the season to climb above Sampdoria and Catania in the league table.
"I tip my hat to our opponents who fought until the end for their point," he added. "But we should have done better managing the final 20 minutes, especially with the chances we created in injury time.
"Sassuolo only looked dangerous to me once, thanks to a mistake on our part, but we never struggled in the entire match."
