The striker, who is unattached after his contract with Championship side Reading expired, made it 2-1 to Wales in Friday's contest at the Stade Pierre-Mauroy with a wonderful turn and finish after captain Ashley Williams had cancelled out Radja Nainggolan's magnificent opener for Belgium.
Sam Vokes capped off a remarkable fightback with an 85th-minute header, ensuring Wales' place in the semi-finals against Portugal next Wednesday.
Speaking after the game, Robson-Kanu - whose performance earned him the man of the match award - said: "We're on cloud nine, we've been working for it for many years.
"It's about nights like this where we've got the rewards and taken our opportunity. We've done the nation proud.
"We've come into the tournament, we were underdogs to qualify but we knew the quality we had. [It's] fantastic to get to quarters but to put in the performance today is a credit to everyone involved.
"It's a quick turnaround [to the semi-final]. We're professionals, we've got another game and we'll take it very seriously so I don't know how much celebrating we'll do."
On the question of his club future he added: "I've been at Reading for 12 years, been very loyal in that time but I made the decision to run my contract down.
"It's important to have my future in my own hands, for me and my family."