• Toffees defender Michael Keane scored the winning goal in the second half, leaping highest at the near post to flick home Lucas Digne’s corner at an empty Carrow Road.
• Norwich boss Farke sprung a surprise by opting to leave out his two most potent attacking threats in Teemu Pukki and Todd Cantwell, who have contributed 17 of the side’s 25 league goals this season.
Daniel Farke says his side “won’t give up” despite it “not being realistic” for Norwich to escape relegation after suffering a third straight Premier League defeat at home to Everton.
The Canaries remain rooted to the bottom of the table, six points adrift of safety, but they retain hope as the three sides above them - West Ham, Bournemouth and Aston Villa - all failed to win on Tuesday and Wednesday.
Norwich are in FA Cup quarter-final action on Saturday, hosting Manchester United.
“I can’t accuse the lads at all today,” said German boss Farke. “I can just praise the workload, the togetherness. In terms of attitude, we showed organisation and I can just give compliments. We don’t give up, for sure. We have seven games and have a chance.
“It’s not realistic for us to win the FA Cup or stay in the league. When you wear this yellow shirt, you have responsibility and big pride. As long as there is a chance, we won’t give up.”
Toffees defender Michael Keane scored the winning goal in the second half, leaping highest at the near post to flick home Lucas Digne’s corner at an empty Carrow Road. The Canaries could have broken the deadlock in the first half but Onel Hernandez’s deflected shot bobbled off the foot of the post.
Dominic Calvert-Lewin forced Canaries goalkeeper Tim Krul into a couple of saves, with victory for Carlo Ancelotti’s side lifting them up to 10th in the table.
Norwich boss Farke sprung a surprise by opting to leave out his two most potent attacking threats in Teemu Pukki and Todd Cantwell, who have contributed 17 of the side’s 25 league goals this season.
Though Hernandez made some early darts forward and also struck the post, the Cuban drifted out of the game while fellow attackers Ondrej Duda, Lukas Rupp and Josip Drmic offered very little.
With just two goals between the quartet this season, the performance from the forward line showed why Norwich are the league’s lowest scorers this season.
Everton goalkeeper Jordan Pickford was a spectator for the second half, and the closest the home side came to scoring was when Drmic headed wide of the post in stoppage time.
Though they still face trips to Arsenal, Chelsea and Manchester City, Norwich have huge games coming up against fellow strugglers Brighton, Watford and West Ham. Results in those will go a long way to determining their fate at the end of the campaign.
Everton signalled their ambitions with the appointment of three-time Champions League-winning boss Ancelotti in December to replace Marco Silva, who was sacked after a string of poor results.
When the Italian took over, Everton were 15th in the table and staring the wrong way - just four points clear of the relegation zone - but their latest victory sees them looking in the opposite direction, four points behind seventh-placed Tottenham.
The thought of clinching a Europa League spot at Christmas would have been wildly unrealistic but is now a real possibility with match-winner Keane telling BBC Sport “it is definitely in our grasp”.
The Merseysiders created few clear-cut openings but took the big chance that fell their way as Keane headed in his second of the season to end a run of four games without a win. The clean sheet was welcome too, having not managed a shut-out in their 14 previous away games, backing up the point they collected against rivals Liverpool on their return to action.
Ancelotti said: “What we needed from this game was three points, the three points arrived and now we can dream to climb up the table. The players satisfied me a lot.”