The La Liga giants looked set for a semi-final berth after winning the first leg 4-1 at home but capitulated in the Italian capital, going out on away goals after a humiliating 3-0 defeat.
Valverde's side return to knockout action on Tuesday with a visit to Lyon and the Barca boss is confident there will be no such complacency this time out.
"The learning of Rome is that you should not let your guard down," he told a media conference.
"In the first leg, you need to have a high guard - we will take this into account.
"When we played Roma everyone said they were a weak opponent, which did not help us.
"We are eager to play because we've been waiting for the game for a while, and we're under pressure because we know the enthusiasm of our fans."
After three successive draws, including a 1-1 result at home against Real Madrid in the first leg of their Copa del Rey semi-final, Barca returned to winning ways on Saturday with a slender 1-0 triumph over Real Valladolid.
Not all supporters are happy, though, with some taking issue with Valverde's tactics after the team managed just two goals in their last three outings.
The Barca boss, who recently signed a one-year extension to his contract , is unfazed, though, and insists his side plays attacking football.
"Everyone has their own opinion," he added.
"We are a team that clearly plays to attack. I do not have much more to say, we'll see on Tuesday."
Lyon's influential playmaker Nabil Fekir will miss the game through suspension and Valverde admits that is a boost to Barca's chances.
"I'm not going to deny that he is a player who can decide any game," he said.
"He is crucial to the offensive game of his team. It is an important loss and we will try to take advantage of it."