Roma had Adem Ljajic to thank at the Stadio Olimpico after the Serbian midfielder scored twice late on to snatch a draw for the hosts, who had Daniele De Rossi sent off five minutes into the second half of the Serie A fixture.
The draw left Roma three points adrift of league leaders Juventus.
Sassuolo raced out to a two-goal lead inside 18 minutes as Italy international striker Simone Zaza ran rampant up front for the visitors.
But Ljajic completed Roma's remarkable comeback in the third minute of injury time before Sassuolo's Sime Vrsaljko was dismissed.
"This team has a soul. If we needed more proof, we got it tonight. It feels like a victory, as to fight back from 2-0 down with 10 men, the lads were just exceptional," Garcia told Sky Sport Italia.
"I can also say Sassuolo proved again they are a team with genuine quality, though we knew that already."
Roma found themselves trailing after 15 minutes, when Zaza charged down a clearance from goalkeeper Morgan De Sanctis.
Zaza was at it again three minutes later as he latched on to Simone Missiroli's ball over the top.
Despite having De Rossi sent off, Roma continued to press and they were rewarded 12 minutes from time, when Ljajic converted a penalty.
Ljajic was not done there, pouncing on Alessandro Florenzi's low right-wing cross, but the 23-year-old was not as buoyant as Garcia post-game with Roma failing to close the gap on Juve.
"It was a difficult match, we ran a lot and played the entire second half a man down," Ljajic told Sky Sport Italia.
"Sassuolo are a very strong side, especially in attack. We got off to a bad start.
"This is certainly a missed opportunity, as we could've gone to within a point of the Bianconeri and did not manage it.
"In any case, there are still many games to play and many points still up for grabs."
