The Stadio Olimpico outfit conceded a late equaliser at CSKA Moscow in the UEFA Champions League on Tuesday, but bounced back to maintain the pressure on leaders Juventus in Serie A.
Inter equalised twice after Gervinho and Jose Holebas gave Roma the lead in the 21st and 47th minutes respectively, before Miralem Pjanic netted twice to settle the contest.
And Garcia says he could not have asked for more from his players.
"You must always respond on the pitch and tonight we did that in every way possible," he told reporters after full-time. "I wasn't worried about today. I know the team is united and can hurt the opposition.
"We conceded from a set-piece and a deflected shot. That means that from a tactical point of view we did well"
The win took on added importance after Juventus scored a late winner to beat local rivals Torino earlier in the day, but Garcia claims he is only focused on his own side.
"It doesn't matter what the other teams do," he stressed. "We just have to keep focusing on ourselves, and we were superb today."
Roma host Manchester City in a fixture that will decide which, if either, of the teams reach the knockout rounds of the Champions League on December 10, but Garcia insists the match is yet to enter his thinking.
"I'm not thinking about City in the slightest," he added. "For now our biggest game of the season is against Sassuolo next Saturday.
"We have to make sure we keep going as we are in Serie A. There'll be time to worry about the Champions League later."
