Inter won 2-0 in Rotterdam to take control of their Champions League round 16 tie with this first-leg away win.
Speaking at the final whistle, Dumfries said: "Getting to the end of the Champions League? I really believe in it, we reached the final two years ago too: anything is possible.
"But you always have to play well, even in defence. We're happy with what we've done so far."
Inter teammate Stefan de Vrij also told the club's TV channel after victory over his old club: "It was a very special evening for me, it was wonderful to come back here and the way they welcomed me. I had goosebumps, I'm very grateful to Feyenoord who are always in my heart."
On the match, he added: "It's an excellent result, they started very strong, we were a bit imprecise. However, together we achieved a good result. We improved during the match, we scored a great goal, it's important not to have conceded and then scored the second. There were dangers, we were facing a great team, they didn't create any great dangers, in the end our quality came out."