Former Liverpool, Chelsea and Real Madrid manager Benitez won four of his first five games in charge of Everton but the team's form has slumped sinceThere was a point in the first half at Carrow Road, when the home and away fans harmonised.
Everton's travelling contingent demanded that Rafael Benitez "get out of our club".
The Norwich supporters predicted the opposition manager was getting "sacked in the morning".
The pitch invader, intercepted on his way from the away end to the dugouts, didn't look like he disagreed with either.
The Toffees' 2-1 defeat means they have lost nine of their past 12 Premier League games, sinking from fourth in the table at the start of October to 15th.
Everton owner Farhad Moshiri has been staunch in his support of Rafael Benitez since the his appointment in June. But how much longer can his patience last?
Benitez running out of excuses
The Spaniard admits he is at the mercy of Moshiri.
"The rest is not in my hands," said Benitez after Saturday's defeat.
Fans displayed banners demanding Benitez's departure during the defeat by Norwich at Carrow Road"I came here to fix issues that were coming from the last five years.
"What I have to do now is analyse the mistakes we are making and make sure we avoid that for the future."
There may be long-term issues, but Benitez needs an improvement in form in the very near future.
Norwich 2-1 Everton: Toffees keep making same mistakes - Benitez"I am disappointed we do not learn," he said. "We made the same mistakes in the past and continue making similar mistakes. We have worked on that but when we are on the pitch we have a little anxiety.
"We are doing things little by little that are good for the future, bringing in and improving players but the reality is we have to win on the pitch."
Fan unrest spreads
Everton fans came prepared. A banner demanding Benitez's exit was seen in the away end in the FA Cup win over Hull last weekend and it was unfurled at Carrow Road after the visitors fell behind to two goals in the space of 94 first-half seconds.
The noise continued on-air and online. Benitez trended on social media. In a bad way. Duncan Ferguson was mooted as a possible replacement.
Former captain Kevin Ratcliffe tweeted that he was "embarrassed" by the performance.external-link
One caller to BBC Radio 5 Live insisted that the appointment of a man who led Everton's cross-town rivals Liverpool for six years was doomed from the start.
BBC Radio 5 Live reporter John Southall said: "There is a lot of anger around Rafa. They are still making mistakes and don't seem to be learning. They lost their way terribly after the first goal.
"Whichever way you look at it, it is a pretty grim situation for Everton. The fans' reaction at the end summed it up. It seems now they have had enough and when you look at the calibre of people they have got, they should be doing much better."
'It's hard to see how Benitez can survive' - analysis
Chief football writer Phil McNulty
Everton's hierarchy have been following their instincts to stick with the manager they gambled so much on in the summer - but it is hard to see how Rafael Benitez can survive the embarrassing loss at Norwich City.
Owner Farhad Moshiri was prepared to ignore Benitez's illustrious Liverpool past - and an ill-judged remark calling Everton a "small club", which rankles to this day - in his belief that he would be the man to bring stability to this dysfunctional club.
It all started well, with good early wins and the success of signings Andros Townsend Demarai Gray but injuries to key figures such as England striker Dominic Calvert-Lewin saw Everton's season go into a tailspin.
Benitez also seems to have lost his way amid some mysterious team selections and a failure to show the sure tactical touch that was always his trademark. The current run is six points from the last 39.
The loss at Norwich merely adds to the growing toxicity towards Benitez and the Everton board, which has already seen the departure of director of football Marcel Brands, and there now simply seems too much anger around the club and with the manager for him to keep his job.
It would be a move typical of the confusion at Everton were they to sack Benitez after he sold France full-back Lucas Digne to Aston Villa following a falling-out and let him spend the £25m raked in on defenders Vitaliy Mykolenko from Dynamo Kyiv and Rangers youngster Nathan Patterson.
Benitez was Moshiri's boldest gamble in his time at Everton. He may now have to take another one.
