Everton boss Roberto Martinez and Norwich manager Chris Hughton were left in disagreement as to whether the 2-2 draw was a fair result at Carrow Road.
The two clubs had to settle for a share of the spoils after four goals in a 20-minute period during the second half.
Steven Whittaker opened the scoring for the hosts before Everton hit back with goals from Ross Barkley and Seamus Coleman.
Norwich debutant Ricky van Wolfswinkel then headed in a 71st-minute equaliser with his manager Hughton declaring he felt his side did enough to warrant a draw.
"I thought it was a fair reflection of the game," he said.
"We were up against a full strength Everton side. If you look at the quality and maturity they've got in the side you can see why they've done so well over the years."
Hughton, who saw his side hammered 5-0 on the opening day at Fulham on the opening day last year, was happy that his players showed the heart to recover after falling behind.
"I thought we showed great character. I thought it was a fair result on the balance of things," he added.
"That's one of the most pleasing things for me. The lad Barkley scored an absolute screamer, but we could have done better with the second goal.
"To go 2-1 down to a team who are as free-flowing in possession showed great character. We got in some really good crossing positions. Overall I was pleased."