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.
"Today 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."
Martinez, following his first game in charge of Everton, disagreed with Hughton's view and felt his side deserved to head back to Merseyside with the win.
"I think overall we deserved the three points," he said.
"But the result reflects the draw because we conceded two soft goals. Overall from a neutral point of view probably we deserved the three points and we did enough."
Martinez's first competitive match did not end in success due to van Wolfswinkel's intervention and the former Wigan boss was happy to acknowledge the Dutchman's achievement.
"That is what he's all about," he said.
"I think as a striker when you get very few chances and you take them it speaks volumes of yourself.
"I thought we kept him really quiet throughout the game but then he scored the chance. It showed he's got a real sense of being in the right place at the right time."
The draw would have been seen as an even better result for Norwich after they lost Robert Snodgrass in the build-up to the game.
Hughton confirmed the Scotland winger returned from international break without any knocks but failed a late fitness test after suffering a groin injury.
"He has a slight groin (problem)," Hughton said.
"We had a big decision to make before the game. He came in yesterday morning and felt it slightly. Fitness test before the game, and we had a big decision to make. If we'd played him he might've been fine but you never know."
Gary Hooper also missed out for the hosts after Hughton had initially hoped the new signing would be back from his shin injury in time to sit on the bench yesterday.
"He's not as close as what we would have liked," he said.
"We feared last week because he was in a fair amount of pain. He has taken a fair whack. We will look to push him and hopefully the weekend."