The Giallorossi have seen questions raised over their character following their goalless draw at Lazio in the previous round and their midweek 3-0 loss at Napoli, a result that knocked Roma out of the Coppa Italia.
"I believe there was a lack of respect for my team after our defeat in the Coppa Italia," Garcia said to Gazzetta dello Sport. "But my team responded in the best way and that was on the pitch.
"We saw a great Roma and we proved that we are strong.
"I have total faith in this team."
Sunday's triumph was Roma's 16th of the campaign and left them nine points adrift of Serie A leaders Juventus although the Giallorossi have a game in hand.
Roma have lost just once this season, a 3-0 defeat at Juventus last month.
"We are second in Serie A," Garcia said. "We are playing incredible football and we are four points ahead of Napoli with a game in hand.
"We have the best defence in Italy and one of the best attacks in the competition, so it means the whole team works well when defending.
"We do not leave spaces for our opponents to shoot.
"I had asked the team to continue seeking results through good football.
"Perhaps in recent games we forgot to play it simple, that is to keep possession and hold out under pressure, but against Samp, we saw more of that."
Roma travel to Bologna next while Juventus host Torino in the Turin derby on Sunday.