City have slumped to within two points of the bottom three after going six league games without a win - and their 3-0 FA Cup loss at Fulham on Tuesday night left some fans calling for Hughton's head.
Further reversals at home to Hull on Saturday and Newcastle on Tuesday would pile the pressure on Hughton, with chief executive David McNally having indicated the manager is doing his job providing he keeps the club out of the bottom three.
Hughton told BBC Radio Norfolk: "The supporters show the passions of their club. We have the same passions here and I am desperate as a manager to make sure we keep making progress.
"We certainly understand and respect the opinions of the supporters. It is their club and one thing I can guarantee is that we are working as hard as we can to be looking upwards."
Hughton remains convinced his side can pull out of their recent slide and regain their form of the previous two seasons, which brought them 11th and 12th-placed finishes.
He added: "In a league that is very tight around we know we're only three points away from 10th place.
"But we want to fight and work as hard as we can to make sure we can start looking upwards."