The Canaries conceded an early goal to Steven Naismith but fought to the end in a tight encounter and claimed a last-gasp equaliser through Sebastien Bassong.
The result came after an impressive win over Manchester United last weekend and extended their unbeaten run in all competitions to seven games.
When asked if his side deserved the point, Hughton said: "I thought we did.
"Over the 90 minutes we had a long time to get back in the game.
"From our standards of late, we conceded a very soft goal and in that first half we didn't keep the ball well enough.
"Everton were the better team over that first 45 minutes.
"But when you are 1-0 down, you have to chase it and ask a little bit more of the players. I think we got that.
"I thought we responded really well. We showed great character.
"I don't think there was masses in it. It was quite a tight affair."
On the downside for the visitors, goalkeeper John Ruddy - who overcame a knee problem to feature - was forced off eight minutes from time with an unrelated thigh injury.
Hughton said the player would need to be assessed but was hopeful it would not be serious.
He said: "We won't know until tomorrow [Sunday]. Hopefully he came off at the right time. I certainly had to make sure I brought him off."
Everton manager David Moyes bemoaned his side's inability to kill off the opposition.
The Toffees continue to ride high in the table but have won just one of their last seven games, a sequence which includes five draws.
Moyes said: "That was pretty hard to take.
"But they were always in the game while it was only 1-0, that is the nature of the Premier League.
"I thought we played well for 25-30 minutes. We started well and controlled the game.
"Norwich grew into the game, give them credit, they had one or two opportunities.
"I thought we had got through the spell and we probably looked more likely to make it 2-0 than for them to equalise.
"But they did and that was it. We came away with a point."
Moyes was also unimpressed with the sequence of events which led to Norwich's equaliser.
He first had an issue with the award of a free-kick against Leighton Baines and then felt John Heitinga and Tim Howard should have done better as Javier Garrido swung in a cross Bassong. Howard might also have stopped the decisive header.
When asked which player was to blame, Moyes said: "A little bit of both. I think the ball was in the air long enough and also I don't think it was a free-kick."
Everton were without Marouane Fellaini, Phil Neville and Seamus Coleman while Darron Gibson and Kevin Mirallas failed to prove their fitness as hoped.
Moyes said: "Today [Saturday] was always going to be a tough game. Norwich have played well and have had some good results.
"With what we had available to us it was always going to make it quite hard.
"It was going to be tight - I couldn't see us winning it that comfortably.
"We were chasing it and we didn't have an awful lot to chase it with. They are the facts."
One positive was the lively performance of Naismith, although the Scot squandered a good opportunity when he failed to find Nikica Jelavic with a pass.
Moyes said: "I hoped he would come here and get six, eight goals. That would be a decent contribution.
"He's now beginning to get a few goals, so good on him."
Naismith arrived in the summer after the demise of Rangers, and Moyes claimed not to know the finer details of the deal.
He said: "There's been no fee at the moment and I don't know the answer. I don't know what 'co' it is - Tesco!"