Canada – 39 places lower than Belgium in the rankings – had earlier missed a penalty as Alphonso Davies’ tame effort was saved by Thibaut Courtois before they were potentially denied two further first-half spot-kicks.
Playing in their first World Cup in 36 years, Canada more than held their own and had 21 shots on goal compared to nine from Belgium.
Englishman Herdman guided Les Rouges back to the world stage following a fine qualification campaign – becoming the first coach to manage at both the men’s and women’s World Cups.
“They showed tonight that they do belong here,” he said.
“It has been a long time since we have been back, our fans were football fans, they really tried to own the stadium tonight.
“They (the fans) walked away proud I’m sure, proud and feeling like we are a footballing nation. We came into the game with a couple of goals, the first was to play fearless and the second goal was to entertain.
“We had some other goals – to create some firsts, but we never got to those moments. I think at times it was one pass too many around the box. I’m not going to criticise them because when you outshoot Belgium I can’t complain too much.
“Sometimes it is your night and sometimes it is not. They made a commitment to themselves before they went out there tonight.”
Herdman revealed astronaut Chris Hadfield spoke to his players before the game but now he needs to bring his squad back down to earth before they face Croatia on Sunday.
“Teams know us now, this is it, the covers are off,” he added.
“We are coming up against a team like Croatia with a midfield three to die for. People will come into the next game respecting us a bit more and knowing what we are about. We’ve got a big effing game coming up against Croatia and we deserve to be here.”
Remarkably, Kevin De Bruyne was awarded the man of the match award despite being far from his best.
The Manchester City midfielder summed up both the Belgium performance and his own display when accepting the accolade in the post-match press conference.
“I don’t think I played a great game,” he admitted. “I don’t know why I got the trophy, maybe because of the (my) name. I don’t think we played well enough as a team.
“We didn’t find any solutions. We started really badly, the momentum was with Canada and we didn’t find a way through their press.
“I don’t think we played a good game today, me included, but we found a way to win and that was it.”