Norwich struck twice in quick succession as an own goal from Michael Keane and a poke home by 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.
Idah told the club website: “We’re really confident as a club. We believe that we’re good enough to stay in this league.
“Everyone played their part today. Whether it was the attackers or defenders, we all did well and we grinded out the result.
“That’s what we needed in a game like today. We need to build on this now and go from here.
“We just need to get as many wins as we can and get as many points as we can.”
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 boss Rafael Benitez.
Supporters expressed their disappointment with the board and manager throughout the match and a pitch invader even attempted to reach Benitez before being caught by stewards.
Everton have now lost nine of their last 13 league matches and Benitez knows they cannot continue to make the same mistakes.
“We didn’t start the game bad in terms of control but after, we made the same mistakes and we made a couple of mistakes in a few minutes and we conceded two goals,” the Spaniard said.
“That is a difficult thing to change in the second half, but we bring onsome players and then the team was much better, we were more dominant, controlled and we had some chances but no clear chances because they were defending with a lot of bodies.
“It’s much better with players coming back. It always makes a team stronger.
“We are really disappointed because we lost. We are disappointed because the fans have been travelling to support the team and it’s not the ideal situation.
“But we cannot change this situation now, we have to learn because we cannot make these mistakes in the future.”