The Uruguayan was installed as head coach at the Stadium of Light in October following Paolo Di Canio's ill-fated tenure.
Poyet has since guided the team to home victories over local rivals Newcastle United and Manchester City in the Premier League, and Ki-Sung Yueng's extra-time winner over Chelsea on Tuesday secured a final-four berth in the League Cup.
And Hughton has backed Poyet to continue moulding Sunderland into a team that reflects his managerial style.
"Gus was a wonderful player, but was always very passionate about the way he played the game and his thoughts on the game, so it was no surprise to me that he went into coaching and management," Hughton said.
"The biggest task for him at Sunderland was that he had a lot of players who had been brought in during the summer by the previous manager.
"Gus' responsibility now will be to put his own stamp on the team and I am quite sure he will do that.
"Sunderland will be boosted to have got through to the semi-finals of the League Cup, but we have to look at ourselves."
Norwich have picked up four points in their last two fixtures courtesy of a win at West Brom and a home draw with Swansea City.
The return marks a good response to a 5-1 drubbing at Liverpool on December 4, but Hughton warned his charges not to be complacent against the team propping up the Premier League table.
He added: "We are on the back of a good performance against Swansea and also off a good away result at West Brom, so we want to keep the momentum ourselves.
"It is always a balance, because you know they have enough good players that if you do not perform, they can hurt you.
"You have to be in the game yourself and give yourself an opportunity to win it.
"You have to set your team up knowing you are away from home, so you have to be resilient enough not to conceded, but also you have to score goals to win it."
