Jacques Brunel's side looked on course for victory over Scotland last weekend when they led 13-3 at the break, only to allow the Scots back into the game with two tries from Alex Dunbar.
Despite letting their lead slip, the Azzurri fought back with a try from Joshua Furno and led going into the 80th minute, but Duncan Weir's last-gasp drop goal secured a first Scottish win in Rome since 2006.
That leaves Italy without a win this year, a disappointing return after last season's fourth-placed finish.
Next up come Ireland, who went down in Rome a year ago, but currently sit top of the table despite defeat at Twickenham last time out.
And Zebre centre Garcia knows his side will have to be much better on Saturday if they are to pick up a first win in Dublin in the competition.
He said: "Our defence was good against Scotland but that's not enough. We made too many mistakes and we can't afford to do that.
"In the first half we held on to the ball a lot, but we played too much rugby in our own half."