Scotland dominated possession in their 13-6 Calcutta Cup defeat but despite hammering away inside the English 22 they could not find a cutting edge.
Italy also experienced that frustration in their defeat to France without being able to fashion any tries in their bright spell while Les Bleus ran in four clinical tries.
And Brunel has called for that sort of efficiency in both attack and defence at the Stadio Olimpico as they seek a first ever defeat of England.
"I'm partisan to playing rugby but sometimes it's stupid when you just play for that aim," he said.
"You lose a match that way, you can't just keep the ball in the 22. The Scots were excessive in that respect and we don't want to go to that excess.
"I don't know if they're not as good but the French backs were very, very efficient.
"They didn't have many chances but scored four tries, we didn't have that efficiency.
"Our aim at international level is that you can't miss more than six to seven percent of tackles but we missed 16 percent in that game.
"We didn't think it would be possible but that was how it went, it's not the character of this team."
Meanwhile captain Sergio Parisse believes the pressure will be on the Azzurri to belie their underdog status for the first match played at the Stadio Olimpico.
An estimated 75,000 fans are expected to attend making it the highest attended Italy home match in the history of the RBS 6 Nations.
And while they have lost all 17 Tests they have previously played against England, Parisse says there is a certainty in the Italian ranks that they will halt that run of results after claiming their maiden defeat of France in last year's Championship.
"We have a big responsibility because it's the first time we're playing in front of so many here in Rome,'' Parisse said.
"A lot of people think that because we're playing at the Olimpico in front of so many people that we must win, but England are one of the strongest teams and it will be very difficult.
"It would be a very important result for us if we win. Beating France at home was a boost for us and the whole of rugby in Italy.
"No one imagined we could do it. Everyone talked about it as a difficult game but no one talked about it as a game we could win. It's different this year, everyone believes that we can win, but it won't be easy.''