Garcia relieved to win after Roma's poor defensive showing
Garcia was able to deploy both Francesco Totti and Mattia Destro in the same starting XI for the first time since their 4-0 win over Catania in December, and the attacking pair both made an early impact, with a goal each prior to the half-hour mark in the Italian capital.
Despite the forward duo impressing as a partnership, Garcia was concerned that his second-placed side in Serie A could not win more comfortably with their early lead.
"We had done many great things but also given away too many chances. We hadn't suffered like this at home for 15 games," he told Sky Sport Italia.
"They say football is the art of making life difficult for yourself but we got the three points and that was the important thing.
"We could've scored more goals but without a great Morgan De Sanctis performance we could've conceded more too.
"We made mistakes and misplaced some very easy passes. That is the problem, as we must be always concentrated and never leave anything to the opposition."
Garcia said Totti and Destro had more impact than simply their goals, with Totti assisting Vassilis Torosidis for Roma's third goal midway through the second half, while several more chances were created.
"We scored three goals and had the chance to score another two or three," the coach said.
"We created a lot in attack, so I am happy with the performance of these players. We knew the captain (Totti) couldn't play a full 90 minutes but he was truly illuminating tonight.
"I am above all happy with the way the team played, as remember we were without Daniele De Rossi, Kevin Strootman and Douglas Maicon."
Udinese sit in 14th in the table, a mere eight points above the relegation zone, but Garcia hailed the resolve of Francesco Guidolin's men in the second half at the Stadio Olimpico.
"They never gave up and usually after going 3-1 up the game is finished," Garcia said.
"It is a reminder we need to be more concentrated and determined all the way to the final whistle."
Udinese assistant coach Fabio Viviani also spoke highly of his players, as they pressured a top-four side away from home right until the final whistle.
"It was a great performance," Viviani told Mediaset.
"Not everyone can play like this away to Roma, scoring two goals and creating many more opportunities.
"Perhaps in previous years we'd have won a game like this without creating as many chances, but it's an unlucky campaign."
Guidolin skipped post-match media commitments, due to suffering from flu.