The former Wigan boss believes there will still be some shock results before the season is out and his side, with its impressive set of youngsters, can push for the top four
Ross Barkley's header proved to be the winner for the Toffees, and even though his team were not always at their best at Goodison Park, the Spaniard feels that the inconsistent nature of the Premier League could still play to his side's advantage.
"If you look at all the results and the games to come, you are going to get surprises. I feel the points tally [to qualify for the Champions League] is going to be at a high level, and that is our aim," he told reporters.
"We are trying to get as close to those numbers as we can. You are not going to be playing fantastically well every game and you have to find those margins to win games.
"Winning when not at your best is a sign of what we have in the squad."
Martinez was particularly pleased with the performance of Barkley, whose header capped off a performance close to the level which he was producing earlier in the season.
The youngster suffered a foot injury in December, with his displays since then frustrating the Goodison faithful, but his manager was thoroughly impressed with the way he acquitted himself against the Swans.
"We faced a really difficult test from Swansea City today and to get the all important three points is a fantastic feeling," Martinez said.
"For young players like Ross Barkley and John Stones it was a phenomenal test, and I thought Ross showed a real tactical awareness against one of the best teams in the league in terms of possession around his area.
"Today we saw a really fresh Ross Barkley. Against Arsenal he played really well and for long spells he showed he was back to his best.
"In every game he takes things on board and develops as a young footballer. We are finishing the season really strong, and Ross, with his age, is going to be one of the players that is going to be strong at this stage of the season."
Meanwhile, Swansea manager Garry Monk was frustrated with the way his side allowed the hosts to score twice soon after the half-time break, and believes they must do better if they are to stave off the threat of relegation.
"When you come to places like this, there’s always a period when the opposition has pressure, and you have to manage that properly," he said.
"We didn’t do that in a five minute period in the second half and it cost us. After that we had a few chances and if we hadn’t given them such a lead we would have been able to come away with something."