Garcia's side were missing talisman Francesco Totti and in-form Gervinho, and were forced to play the final half hour with 10 men after Maicon's sending off.
Despite his dismissal Roma managed to improve their game and thoroughly deserved their victory courtesy of American Michael Bradley's 82nd minute winner.
"All of our players are important. Today we were without the captain and Gervinho, and I always say that someone who is on the bench today can be a starter tomorrow," Garcia said after the match.
"Whoever puts the work in during the week will see things go their way."
Garcia is cutting an increasingly confident figure on the Roma bench and is looking more comfortable in front of the cameras as each week goes by.
Having learned Italian quickly he is fielding questions in a manner that inspires faith.
There is little doubt now, too, that his team are genuine scudetto contenders, having equalled Juventus's record of nine consecutive wins at the start of the 2005-06 season.
"The strength of my team is that it believes in itself, that it moves forward, and that's even more important in a match like today's," added the Frenchman.
Even more impressive is the way he has organised his team, who have now scored 23 goals conceded only one in the league this season.
They needed that defensive solidity on Sunday against an Udinese side who are strong at home and, although Luis Muriel hit the post after three minutes, they mostly restricted the hosts to half chances.
At this point last season Roma were already in the middle of a crisis after throwing a two-goal lead away to lose 3-2 at home to Udinese, their third defeat of the season and the second time that they had given up such a lead. Rumours of dressing room unrest were rife.
This season everyone is working together, attacking and defending as a unit, the key to their remarkable start to the season.
"We won at a very difficult ground. They've not lost here for a year and we were down to 10 men," said Garcia.
"This is really great thing for us and I think that it will be very important in the future."
(Editing by Josh Reich)
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