The Giallorossi were no match for Napoli and fell 3-0 in Naples to lose 5-3 on aggregate in the semi-final stages.
"Napoli deserved to win," Garcia said.
"They were in better condition than us and they showed it.
"We made too many mistakes in both legs and we didn't make the most of our chances but they did.
"We are disappointed because we wanted to reach the final but we have to accept the result.
"We should have done better.
"Now we must turn our attention to Serie A."
Roma are second in the standings, nine points behind Serie A leaders Juventus but have a game in hand.
The Giallorossi were held to a goalless draw by Lazio in last weekend's Eternal City derby.
Roma captain Francesco Totti and striker Alessandro Florenzi are expected to return to the starting line-up having come on as second-half substitutes against Napoli.
Rivals Sampdoria are 12th in the standings, 23 points behind Roma, but coach Sinisa Mihajlovic has not ruled out his team pulling off a surprise.
The Blucerchiati travel to the Stadio Olimpico on the back of Sunday's 1-0 victory over Cagliari, their second straight win.
The outcome extended Samp's gap over the relegation zone to 11 points.
"Our aim is to avoid the drop and we are on the right path to achieve it," Mihajlovic said.
"Roma are a very strong side but in football you never know.
"We will try to prepare this game in the best possible way and go there determined to get a positive result.
"It's not an impossible game because there is nothing impossible in life."
Samp have not won three consecutive league games this season.
The visitors will be without striker Maxi Lopez, who is out with a muscular injury, but welcome back defender Shkodran Mustafi from suspension.