In draining conditions in Miami, the Three Lions fell behind to Andreas Schjelderup's opener, before the in-form Jude Bellingham equalised just before half-time.
Bellingham again stepped up in extra time, to fire home from close range, but it was a nervy end for England, despite dragging themselves over the line once more at this tournament.
Norway had a penalty shout rejected, a goal ruled out for a foul after a VAR review, and the ball appeared to hit the stadium's overhead 'spider cam' in the build-up to Bellingham's first goal.
All of those near misses added to Tuchel's frustration at full-time as he claimed England were lucky to get through to set up a semi-final date with old foes Argentina.
"We made life very, very difficult for ourselves today.
"The result is fantastic. The last four is amazing, but I'm not happy with the performance.
"The commitment is there, but it made life very, very difficult for us in the way we played, how we played, sloppy, lots of safety, not fast enough, not enough. We were lucky today."
However, Tuchel's feelings were not echoed by star man Bellingham, who suggested his manager's did not understand how tough it was for the players out on the pitch.
"Yeah well, whatever. It's a tough shift, so my thoughts and my appreciation goes to the players who've put a tough shift out there.
"Maybe he doesn't know what it's like to play in these type of conditions against Erling Haaland, Odegaard, Nusa, Sorloth, you know. That's not an easy team to play against."
World Cup 2026
The 2026 World Cup will be held from June 11th to July 19th in the United States, Canada and Mexico. The tournament will feature 48 national teams and will be played in 16 modern stadiums.
Match schedule and times | Draw | England at the World Cup | Bellingham: England 'shouldn't fear anyone' | How to watch the World Cup | Predictions and odds
