Abraham struck in Thursday night's 1-1 draw with Vitesse at the Olimpico to reach the final eight 2-1 on aggregate.
“I have to give credit to my team, together we had a good game against an excellent opponent, we all fought and had already seen in the first leg how tough it was," Abraham told Sky Sport Italia.
“This victory was important for us and for the fans. It wasn't our best performance, but we scored and went through."
His strike means Abraham is on 21 goals in all competitions in his first Roma season, the same as legends Gabriel Batistuta and Vincenzo Montella.
“I see it all over my Instagram every day! My only objective when I arrived was to score and help the team, I hope to score many more.
“There's nothing better than scoring and seeing how the fans react."
On the quarterfinal draw, the former Chelsea striker concluded: “Whoever comes our way, we have to be ready. Leicester? Why not a Premier League team? The lads and I will be watching the draw tomorrow."