Fellaini and fellow substitute Dries Mertens came on to score as Belgium became the sixth team to claim a come-from-behind win at the 2014 FIFA World Cup.
The Manchester United midfielder praised the character of Marc Wilmots' side and said they deserved the three points in Group H.
"I'm just glad that one went in though because we were beginning to run out of time, and it was important we took one of our chances," Fellaini told FIFA.com.
"In the end, I think we got what we deserved. We started very nervously and played badly in the first half.
"But I think you saw the character of this team in the second half. We just needed to stay calm, make the right decisions, and doing that got us this fantastic result."
Fellaini endured a disappointing campaign with United, but said he never stopped believing he could produce.
"I always believe and I thought that, yes, if the coach gives me the call, I can help us win this match," he said.
"One thing I know is that if my team-mates put crosses in the box for me, I can score goals. And you saw it today.
"Three times the ball came in for me and every time I won the header. I could have had a hat-trick."
