The 4-1 scoreline was convincing - and it would have been 4-0 had Ricardo Rodriguez not scored a free-kick with the final action of the match.
But after an own goal from Rodriguez, a header from Seamus Coleman and a penalty from Leighton Baines right at the start of the second half made it 3-0, Wolfsburg laid siege to Tim Howard's goal.
The American pulled off a string of saves before the Toffees rubbed salt in Wolfsburg's wounds by grabbing a fourth on the break through Kevin Mirallas.
It was Everton's first European game in five seasons, and manager Martinez said: " We were looking forward to the environment and a European night at Goodison under the lights
"There's been a lot of talk from the fans and it was phenomenal to get that feeling
The atmosphere was perfect for us to start a very good performance
"I thought there were two very good sides
On the night the scoreline probably doesn't reflect the difference between the two sides
"We scored at the right times
Our work-rate was magnificent
We had to defend and we did that really well but every time we went forward we had a clinical touch about us."
Wolfsburg boss Dieter Hecking described Group H as the toughest in the competition, with Lille and Russians Kuban Krasnodar making up the quartet
It was Martinez's first experience of European football, while the majority of the side had never played in Europe for the Toffees before
Wolfsburg only missed out on qualifying for the Champions League by one point but Everton looked completely at home
"It felt really natural, which I think is a real strength of our group," said Martinez.
"We've got a perfect mixture of young players and really experienced players and I do think tactically it was a real opportunity to test that.
"The flexibility that we showed was very good
Wolfsburg were pressing in numbers and really high up the pitch and it could have been very easy just to stop playing and not embrace that but I was so impressed with the manner we held our shape and were able to get forward and use the space.
"We got the fourth goal on the break under massive pressure
We had a real maturity that is really satisfying because going forward that's an area we need to make sure we use in our domestic competitions."
Martinez praised the performance of Howard and felt the keeper's heroics deserved a clean sheet.
The Spaniard said: "I thought he was magnificent
His concentration, the way he controlled his 18-yard box
You would expect once we scored the second and third goals that Wolfsburg would throw everything at us
"It's just a real shame that the last kick of the game ends up in the back of the net
In my eyes Tim's performance is like a clean sheet and that's the way I'm going to keep it."
Hecking accused his team of being naive in the way they allowed Everton to score goals at crucial times.
He said: "It's obviously not the start we'd hoped for
We were lacking in certain areas, both in terms of finishing and defensive work.
"We should have gone into half-time a goal down and we got hit with a second just before the break
Straight after the restart, 3-0 down and the game is lost.
"We really weren't smart enough and showed a certain naivety."
Source: PA