"We were the bookies' favourites to go down," he acknowledged after Saturday's dramatic win against Wimbledon.
"But we are definitely not having a relegation battle this season because we have too many good players and too much character.
"We are not getting carried away over two games and we are going to lose games during the season but definitely not a long series of games to get ourselves into trouble."
"Scoring so late makes it more of a celebration and everyone goes home even happier," added Noel-Williams.
"Thank God one of the defenders put the goal away and it's happy days at Stoke.
"The gaffer has said we have to have a work ethic in every single game and then our individuality has to come out.
"Playing up front with Carl Asaba and Chris Greenacre is a pleasure. I don't have to look up because I know where they are.
"When we were 1-0 up there was always a chance they could score but we knew if they could score one we could always score two."