The Toffees have lost nine of their last 13 Premier League matches.
Rafael Benitez insisted he came to Everton to “fix issues” that had arisen over the last few years after the 2-1 defeat at Norwich piled more pressure on the Spaniard.
Everton travelled to Carrow Road without a league win since the start of December and defeat against a Norwich team which had been on a six-match losing streak without scoring a single goal will not have eased tensions between the fans and the manager.
The supporters were calling for the Spaniard to leave the club before the game, with banners held aloft, and two goals in quick succession from an own goal from Michael Keane and Adam Idah put the home side on course for a coveted victory.
Richarlison pulled one back for the visitors shortly after coming on with a perfectly-timed overhead bicycle kick but it was not enough for the Toffees to get something out of the game.
“I am a professional and I have enough experience,” Benitez said, when asked if he was concerned about the implications the defeat could have for his future at Goodison Park.
“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 void that for the future.
“The rest is not in my hands.”
The fans expressed their disappointment with the board and manager throughout the match and a pitch invader even attempted to reach the manager before being caught by stewards.
Everton have now lost nine of their last 13 Premier League matches and Benitez knows they have to improve.
He added: “We are disappointed, like the fans, and we have to improve things on the pitch, to do this is to keep working hard, to have all these players coming back and to be sure we make the right decisions and try to be better like we did in the second half.
“Overall you can see this team react but we have to be more proactive and we cannot be losing games and conceding quickly.
“We have to react and the important thing is the team is reacting and they care and they try but the bad thing is these mistakes are costing us games and points every week.”
It was Norwich’s first victory in the top flight since their 2-1 win over Southampton on November 20 and lifts them off the foot of the Premier League table into 18th place, although Newcastle and Burnley have games in hand over the Canaries.
Boss Dean Smith said: “Really proud of the players because they gave it everything.
“I said to them before the game ‘it’s not the be-all-and-end-all game’ but we are getting that way and it’s time for actions rather than words.
“We wanted to get our fans behind us by putting in a performance and showing the energy and verve that we needed and I thought we did that.
“I said at half-time that Grant (Hanley)’s block in the last minute, he put in a captain’s performance where all of us wanted to follow him and I thought we deserved to go in (up) at half-time.”