Canada ended with 21 shots to Belgium's nine as they pushed the team ranked second by FIFA all the way in their first World Cup match for 36 years.
"They showed tonight that they do belong here," said Herdman. "It's been a long time since we've been back here. Our fans were football fans but tried to own the stadium tonight.
"We came into that game with a couple of goals: to play fearless and to entertain. We had some other goals, which was to create some firsts but we never quite got to those moments.
Hardman added in a separate television interview: "I told them they belong here and we're going to go and 'F' Croatia. That's as simple as it gets."
He also revealed that former astronaut Chris Hadfield gave the players an inspirational pre-match team-talk.
"He had a good chat, talking about his experiences representing the country in the military and as an astronaut and I think he inspired them tonight to commit 100% to whatever the strategy was," Herdman said.
Kevin de Bruyne was given the official man of the match award despite an underwhelming display and he said: "I don't think I played a great game. I don't know why I got the trophy, maybe because of the name."
His coach Roberto Martinez said the performance was technically the worst of his six-year tenure, yet added that Belgium were worthy winners.
"Was it technically the worst performance? Yes. The worst game? No, because it's a win at the World Cup," he said. "We had to show a different side of our game and had to defend really well.
"And we took a very good goal. You need to give huge respect to Canada's performance and what we did is that we didn't do well what we were supposed to do while they did well what they were supposed to do. But we deserve the win."
Information from Reuters was used in this report.