Mattia Destro's brace and a Miralem Pjanic free-kick saw Roma continue their fine Serie A form, with Garcia's men still four points clear of third-placed Napoli but well behind leaders Juventus.
Garcia said his side proved their critics wrong after many questioned them following their Coppa Italia loss to Napoli.
"I think that after the Coppa Italia there was a lack of respect for my team," the Frenchman told Sky Sport Italia.
"Today we saw the response, as the truth is always on the pitch. We saw a great Roma side, who are second in Serie A, play incredible football, are four points ahead of Napoli with a game in hand.
"Tonight we proved that we are strong. You all know there was a lack of respect.
"People need to acknowledge what this team can do and say the truth. I have total faith in this team and I think I am right to do so."
Destro headed in an Alessandro Florenzi corner just before half-time to put Roma ahead at the Stadio Olimpico.
Pjanic doubled Roma's lead nine minutes into the second half with a 30-yard free-kick which found the bottom corner.
The three points were sealed three minutes later as Destro's finish from inside the area completed a fine team move, with the visitors reduced to 10 men late on when Daniele Gastaldello saw red.
Garcia paid tribute to Destro and hopes right-back Maicon, who was substituted in the second half, is not set for a spell on the sidelines.
"Destro is a great striker. He is a very important player in my squad, has scored six goals this season and deserves compliments," Garcia said.
"We need everyone and hope Douglas Maicon's injury is not serious.
"Now we have to rest and prepare for Bologna. This week we can sit back and watch the others play in Europe, which will be of great help for Roma to reach the Champions League."
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