Earlier Giovanbattista Venditti had scored his first international try before Tommaso Benvenuti intercepted a speculative Ben Foden pass to put the Italians 12-6 up at the break.
And Brunel warned his side that they cannot afford to make the same mistakes if they are to compete at the highest level.
He said: "The team was doing really well and we were playing our game, then in ten minutes we conceded eight points.
"That's too much for any team. We need to grow to control games of this intensity and when, like today the score is so close.
"And we have to be more accurate with our kicking. We left too many points out there for this level.
"The scrum was very tough. I think that both our, and their packs are very strong in many respects. Sometimes we won, sometimes they did. Sometimes it was even. It was a battle for the whole game.
"But to get the results we have to wait. I'm certain that we have to judge the team on the whole tournament, not just one or two games."