Totti had been out for five weeks but took just 21 minutes to get himself on the scoresheet.
The veteran's partnership with Mattia Destro, who scored on 29 minutes, was also a feature as they played together for just the second time this season.
While Roma were forced to hold on in the end as Udinese battled back - the hosts indebted to goalkeeper Morgan De Sanctis - Garcia was pleased to see his side get back to winning, and scoring, ways after failing to do either in their previous two matches.
"We scored three goals and had the chance to score another two or three," he told Sky Sports Italia.
"We created a lot in attack, so I am happy with the performance of these players. We knew the captain couldn't play a full 90 minutes, but he lit up the game.
"I am above all happy with the way the team played, as remember we were without Daniele De Rossi, Kevin Strootman and Maicon."
Garcia admitted the match had been one of Roma's toughest at the Stadio Olimpico since he took charge last summer.
Roma are unbeaten in 15 home games in the league this season but must continue to maintain that form with Napoli breathing down their neck in the race for the second direct Champions League. Rafa Benitez's side won 1-0 at Torino on Monday night.
"We had done many great things, but also given away too many chances. We hadn't suffered like this at home for 15 games," Garcia said.
"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."
Udinese made their late rally thanks to second-half goals from Giampiero Pinzi and Dusan Basta either side of a Vasilis Torosidis strike.
Assistant manager Fabio Viviani thought his side deserved to take something from the game.
"It was a great performance," he told Mediaset.
"Not everyone can play like this away to Roma, scoring two goals and creating many more opportunities.
"We never gave up and had the chance to snatch a result right at the death, which would've been deserved."