Bronze was due to enter the contest in the final 10 minutes of the contest at Bramall Lane.
Despite being ready on the touchline, Bronze was forced to return to her seat in the dugout as Lionesses coach Sarina Wiegman brought on NJ/NY Gotham defender Jess Carter.
It was later revealed England failed to include Bronze on their official team list.
According to the International Football Association Board's (IFAB) laws of the game, 'only the players and substitutes named on the team list may take part in the match upon their arrival.'
For those who are not named on the team list as a player, substitute or a team official, they are classified as 'an outside agent'.
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Wiegman confirmed the administrative error in her press conference after the match.
"Yeah, unfortunately that was a human error," Wiegman said.
"That's us, we're all one. That was a human error from our side.
"That was very frustrating of course and very disappointing because we wanted to bring her in.
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"Things happen sometimes."
Luckily for the Lionesses, the administrative error mattered little as they beat Switzerland 1-0 thanks to Grace Clinton's 8th-minute strike.
Clinton was on hand to smash home the rebound after Millie Turner headed the ball onto the post from a free-kick.
The Manchester United duo were two of 10 changes made by Wiegman to the team that drew 0-0 with the United States at Wembley last Saturday.
Clinton was also one of four 21-year-olds who started the contest alongside Laura Blindkilde Brown, Ruby Mace and Aggie Beever-Jones.
Speaking after the contest, Wiegman was pleased with how her young stars played but lamented the team's drop-off in the second half.
"I thought in the first half we played really well, we challenged them all the time, we played mainly in their half of the pitch, created chances, scored one goal," Wiegman said.
"I was really happy with that because what we wanted to do, with a very young team, some debuts (Blindkilde Brown and Mace), some starts for the first time (Beever-Jones), one starter that hadn't played for us in six years (Gabby George), so many changes, but I thought that was a very good half.
"I think the second half our level dropped, we were more sloppy, we didn't find the box well enough. They did some different things, but I still think we were not as good aligned as we were first half.
"I think you can tell that for some it's the first time. You have to get through these moments, become more comfortable, and everyone's different.
"So some were maybe a little more anxious than others, but that's OK, you have to get through, and now it's 'OK, how are you going to move forward, how quick does the development go?' And that's what we see also with some other players who are now more starters than they were a couple of months or years before."
The Lionesses return to action on February 21 when they take on Portugal in their first match of the Women's Nations League.