Brazilian full-back Maicon earned a point for second-placed Roma at the Stadio Olimpico, with his strike 12 minutes into the second half cancelling out Massimo Maccarone's 39th-minute penalty.
Roma were reduced to 10 men in the 37th minute when Kostas Manolas saw red for a professional foul on Riccardo Saponara and Maccarone converted the spot-kick.
Empoli also went into the break with a man less after Saponara was shown a second yellow card in first-half stoppage time.
The home side levelled proceedings in the 57th minute, with Maicon finding the bottom corner of the net as Roma ended the match six points adrift of leaders Juventus.
"When we are in a difficult moment with so many problems, we can only praise the reaction of the team," Garcia told Sky Sport Italia.
"Not only were we a goal down and a man down, but in the second half we stepped up the tempo and did everything to win.
"[Davide] Astori hit the crossbar, [Juan] Iturbe went off, so let's just say at the moment luck is not on our side."
Garcia added: "The reaction in the second half was that of a great team. We proved that we know the right path in terms of tactics, quality and physicality. We do know that we should push more from the start.
"I think our fans are happy with the second half. They want to see the whole game like that and above all to win. We are working on it.
"We know things will go better when I have more choices at my disposal."
