Bellingham was the star of the show with both goals - the second in the third minute of extra time - as England overcame the extreme Miami heat to come from behind, banking his fourth man-of-the-match award from six games.
They will now face Argentina, who also needed extra time to overcome Switzerland 3-1 in the later quarter-final on Saturday (Sunday AEST).
Tuchel's England had to do it the hard way against the Scandinavians, requiring extra time to eventually book their fourth World Cup semi-final, and the German said he was "not happy with the performance".
Real Madrid star Bellingham challenged his manager's view.
"Maybe he doesn't know what it's like to play in those kind of conditions against Erling Haaland, (Martin) Odegaard, (Antonio) Nusa, (Alexander) Sorloth," Bellingham said.
"That's not an easy team to play against.
"So, I think we've tried to create a positive environment.
"We should continue that going into the final four. I can't speak highly enough of the lads.
"You're not going to win every game, popping the ball and making a thousand passes. Sometimes you have to win dirty, and we've done that again tonight."
Tuchel responded to Bellingham's comments and insisted there is no disconnect between himself and the players.
"Absolutely, no one disputes that. I am impressed with the shift that they put in," he said. "The effort, team spirit, the belief and to overcome adversity and to dig in and find ways to win is on the absolutely highest level.
"But I'm also a football coach and I think we can play better. In general, I think it was not a high-level game."
The 23-year-old Bellingham drew level with his captain Harry Kane on six goals for the tournament, having almost single-handedly dragged his side through with a second successive brace.
"I'm a confident boy, but I don't think you go to bed at night dreaming about games like that," he said. "It's nice to have an impact and to help my team, but my god, the effort of those lads in there."
Andreas Schjelderup opened the scoring in the 36th minute for Norway with a shot that caromed off the right post.
But Norway's superstar striker Haaland was kept off the scoresheet for the first time this tournament. The Manchester City star sat dejectedly on the bench after being subbed out in the second half of extra time.
"It was not a tough decision to take him out," Norway coach Stale Solbakken said.
"He was finished. Maybe I should have taken him out 10 minutes before. He also got a dead leg in the second half, so that combined with the fatigue. He did everything he could."
Bellingham's equaliser from close range in first-half stoppage time elicited a roar from a crowd that included Mick Jagger and David Beckham.
Moments beforehand, a Norway goal kick resulted in the ball appearing to make contact with an aerial camera cable before landing at the feet of England's Elliot Anderson.
The ball was eventually played to Bellingham, who beat Orjan Nyland with a low shot to the far post. By rule, if the ball had been noticed hitting the cable, play would have stopped and a drop ball would have been used to determine possession.
"That was unlucky for us," Solbakken said. "The ball fell straight down from the sky, so it changed its direction. It became a misunderstanding among our players."
But FIFA said its "heartbeat of the ball" technology showed no peak when the ball was in the air "and therefore no evidence that the ball touched the overhead wire and changed the movement of the ball".
Norway nearly went ahead 2-1 in the 56th minute when Torbjorn Heggem put a rebound past goalkeeper Jordan Pickford after a corner kick. Following a video review, the goal was disallowed because of a foul by Haaland in the box.
- with PA
