Barca went 2-0 up thanks to own goals from Daniele De Rossi and Kostas Manolas, before Gerard Pique added a third and Luis Suarez
scored his first Champions League goal of the season after Edin Dzeko had pulled one back for the Italians.
Commenting on the nature of the win, Valverde said: “Football is a game of errors. You want to make your rivals commit them and to avoid them yourself. We all want our players to be perfect and never make errors but we all do. Even coaches.
“During the season there are all types of games. Ones where you merit more than you get and ones were you get more than you merit. We scored the goals we merited, they attacked us and got the goal they were looking for, which made our fourth very important.”
Barcelona have profited from five own goals this season, a Champions League record, although defender Pique said it was not down to luck.
“It’s not just luck that we get own goals in our favour. Things happen for a reason. I think that if these goals go our way it’s because we press high, we push up in attack – the ball is in the opposition area more than usual in other teams’ matches.
“We played a terrific game. Probably we’d feel better if we hadn’t conceded but we take a decent advantage to Rome.”