The Canaries hit a late double to come from behind and beat Everton 2-1 at Carrow Road on Saturday, which was a first Barclays Premier League win since December 19.
The victory moved Norwich some eight points clear of trouble heading into the final 11 matches of the campaign, which continues at leaders Manchester United on Saturday.
Hughton's first season at the helm opened with four defeats from the first seven league outings and was then followed by a remarkable 10-match unbeaten run, which included home wins over Arsenal and United.
Although Norwich now look capable of breaking the fabled 40-points barrier soon enough, Hughton would rather have been through less of a rollercoaster ride.
"The teams that can be that consistent are the teams that are used to this division, have the quality and are regular members of the division. We are still striving to be that and along the road with that come the inconsistencies," said Hughton, who took over when Paul Lambert left for Aston Villa in the summer.
"The spirit has never been lacking. It has been there all season, but this is a tough league to get wins.
"We play a tighter game and so perhaps it is difficult to get the wins we want.
"However, in the end, there is only one thing that matters and that is come the last game of the season, we have enough points to still be in this division."