After Steven Naismith and Romelu Lukaku had given Everton a first-half lead at Goodison Park, Mikel Arteta put through his own net against his old club as the hosts took control in the battle for the final UEFA Champions League spot.
The result leaves Martinez's side a point behind Arsenal with a game in hand as they look to qualify for the competition for the first time since 2005.
And the Spaniard, in his debut season at the club, was full of praise for his side, describing their performance as "phenomenal".
"In terms of the satisfaction you can get as a manager, that was as good as it gets. I thought the performance was, from the first minute until the last, very strong in every department," he said.
"The way we wanted to play today we had to be perfect and I think in every area the players were phenomenal."
Everton's most recent outing in the Champions League came to an early end when they were beaten by Villarreal in the third qualifying round nine years ago.
Since then, they have been limited to appearances in the UEFA Cup and the UEFA Europa League.
The Arsenal result once again confirmed that under Martinez they are a serious force in the Premier League, but the Spaniard refused to be drawn on comparisons with other key games for the club.
"Playing against a top-four team at this stage of the season - we've never had that demand," he added.
"It was a different challenge so I think it would be very unfair to compare this performance to another one because the implications today were quite unique.
"I knew that if we could get the three points it would leave us with 63 points, which is an incredible return at this stage of the season, but we've still got 18 points to fight for.
"If from now on we don't pick up any points we're not going to achieve our aim.
"Yes, it was a great performance and they were three huge points from a psychological point of view but we face Sunderland at the weekend and if we're not perfect in that game we are not going to get three points."
