Norwich were 4-0 behind at half-time thanks to a Bradley Johnson own goal, as well as efforts from David Silva, Matija Nastasic and Alvaro Negredo.
Yaya Toure, Sergio Aguero and Edin Dzeko completed the rout after the break, as Norwich's plans for damage limitation fell flat.
And Hughton was unreserved in his apology to the Norwich fans.
"We all let the club down today," he said. "I'm manager, I pick the team and I determine the tactics of the team.
"The message (to the fans) is that we have very much let them down, but they are a wonderful support.
"They would have been entitled to be on their way back to Norwich well before the end of that game, but they stick very much by the team and the club.
"We conceded early goals which I think put us on the back foot and perhaps made us a little bit nervous and, with a team like Manchester City, you can't afford to do that.
"What it perhaps does show is that absolute quality that they've (Manchester City) got.
"We found it incredibly difficult to handle them and that being the case, you've got to make sure you defend and defend well.
"We weren't able to do that and consequently we suffered certainly our biggest defeat."
Despite the result, Hughton reiterated his belief in his ability to take the club forward.
"I've always had a confidence in my ability and with the group of players that are in that changing room," he added.
"But we need to change and we need to address this one quickly.
"It's early in the season, but we are on the back of a real heavy defeat and I know how that makes everybody feel.
"It's uncomfortable having to speak about the result that we've just had, but you have to bounce back from it."
