Our 11th place finish was actually very deceptive. With 2 games left of the season we were still in a lot of danger, but fortunately we went and beat West Brom of all people in our penultimate game, which ensured safety, and then we won again on the final day of the season which got us up to 11th. The 11th suggests to an outsider like yourself that it was comfortable, but it certainly wasn't.
But ok, fair enough, we finished 11th. We then went and spent about £30m on new players, including £13m on new strikers, who managed 9 goals between them all season, and only 1 of those was from our record signing. Hughton didn't have a clue how to use van Wolfswinkel, even though he'd spent £9m. RvW showed in his first few games that he is quality, however he slowly went downhill, and by the end he was a liability. Which is partly Hughton's fault, and partly his own. But do you honestly think it's good enough for a team that in your view comfortably finished 11th the season before, to be in 17th with a few games left, with the teams below having games in hand.
I agree the timing of the sacking was poor, as I've said, he should've gone earlier. However, to say we should've stuck with him is ridiculous. Our first game after Hughton was sacked was Fulham away. Under Hughton it was an absolute certainty that we would've lost, as we'd lost our last 8 away games before that one. We needed to get someone else in, anyone else, as they would give us a much better opportunity of winning. As it goes, we went to Fulham, and completely outplayed them, and had it not been for an unbelievable Stockdale save in the first half, we would've gone 1-0 up, and probably gone on to win the game. As I said though, he made the save, Fulham got a goal from a set-piece, and despite our best attempts we couldn't salvage anything. Under Hughton we would've been dead and buried at that point, but we went there with Adams and were unlucky not to win.
You even say in your post "I remember the game against us on the last day of the season and we were by no means convincing in victory. As a Norwich fan has pointed out, they could have got something against Liverpool. They drew with Chelsea". Exactly. You've proved my point. We were much better under Adams in the last few games against difficult opposition, than we would've ever been under Hughton, that's why he was sacked.