The Toffees sacked manager Roberto Martinez on Thursday after the 3-0 loss at Sunderland which consigned Norwich to relegation.
Neil, who is yet to fully commit to the Canaries but has hinted at staying, said: “For me, and hopefully for the squad, it’s about pride.
“Not only that, for the amount of support the fans have shown us all season, particularly the away fans, we owe them to go out and do our very best.
“That is exactly what I would expect.”
Asked if it would be difficult for his players to rise to the challenge at Goodison Park, with the crushing disappointment of relegation still raw, Neil was dismissive.
He rapped: “If it is difficult for them to raise it, we’ve got some of the wrong people here.”