Having failed to win in any of their previous five games, Liverpool arrived at Carrow Road under pressure on Saturday, but they made light work of the home side, strolling to a 5-2 win thanks largely to the performance of Luis Suarez.
Suarez scored a sublime hat-trick, but his task was made much simpler thanks to some terrible defending from the hosts.
Slack Norwich marking made life easy for Suarez in his first and third goals, and Michael Turner gifted the forward his second by dithering on the edge of the box, allowing the former Ajax man to pinch the ball and beat John Ruddy.
With Chelsea and Arsenal next up, the Canaries are in serious danger of slipping to the foot of the table, and Hughton, who replaced Paul Lambert as manager this summer, has warned his team they must perform better if they are to get out of the relegation zone.
"You obviously are concerned the longer it goes on, but you have to get a response and you have to demand that from the players, irrespective of where the next game is or who it is against," Hughton said.
"This season is not over. It's not about six, seven or eight games, it's about a season's worth of games.
"We need to make sure we are picking up the points and the sooner the better for us."
The Norfolk club, who finished 12th under Lambert last term, regrouped after a similar mauling on the opening day of the season at Fulham and Hughton hopes the same will now happen following Saturday's defeat.
"We had a similar defeat in the first game of the season and we got a really good reaction from the team then so we are going to have to have that again," the former Tottenham coach said.
Although they were winless before Saturday's trip to Carrow Road, signs that they Merseyside club were finally clicking under Rodgers came last weekend when they dominated, but ultimately lost, their game against arch rivals Manchester United.
The Reds were a class apart from Norwich in all quarters on Saturday, but Rodgers must take pride in particular from the way his youngsters performed.
Teenage trio Andre Wisdom, Suso and Raheem Sterling all showed flashes of brilliance while Nuri Sahin operated superbly just behind Suarez in the hole.
Rodgers felt his team had been threatening to put on such a performance for a while.
"I'm not surprised because our performance levels up to now have been very good apart from one game against Arsenal and when we were down to 10 away at West Brom," Rodgers said.
"Our play was outstanding. In the last couple of years it has been a difficult place to come and get a result so to arrive here and score five goals and play like we did was outstanding."
Norwich, meanwhile, will take comfort from the fact that two of their key players, Sebastien Bassong and Anthony Pilkington, look set to return for next week's game at Stamford Bridge.
"Bassong wasn't available, but we hope he'll be back for next week," Hughton said.
"Pilkington didn't react (to his treatment) as good as we thought but we hope he'll also be back next week."