Roma needed just the one goal to see off Shakhtar Donetsk on away goals, Edin Dzeko decisively striking early in the second half.
Edin Dzeko credited his Roma team-mates for a "patient" performance as they dumped Shakhtar Donetsk out of the Champions League.
A 1-0 win, after a 2-1 defeat in Kharkiv, took Roma through on away goals as Dzeko scored seven minutes into the second half with the game's first chance of note.
And although the Serie A side were outplayed for long periods at Stadio Olimpico, the Bosnian praised the way his side did not panic before eventually finding the breakthrough.
"It was a great night for me, for Roma and the whole club," Dzeko told UEFA.com. "We deserved this.
"We were patient. We knew that one goal could see us reach the quarter-finals. We scored that goal and then we did everything all together.
"I did [think a second effort was in] but the ball somehow went wide of the goal. That [one that went in] was the golden one.
"I'm proud of this team because I think we knocked out a very strong team."
He added: "Everyone deserves a standing ovation because we all gave absolutely everything, right up until the last minute. We deserve to go through, to be in the quarter-finals."
And Roma legend Francesco Totti also congratulated his former side on Twitter.
"A fantastic result, a fantastic Roma: among the best eight sides in Europe," he posted. "We push forward onto the next round."