The Spaniard, however, is still refraining from making any bold predictions about where they might finish this season.
The Toffees moved up from fifth to fourth in the table after beating Southampton 2-1 at Goodison Park, swapping places with Liverpool, whose defeat at Chelsea later on Sunday afternoon ensured the two Merseyside clubs will be in those positions come the beginning of January 1.
With all teams having now played 19 of their 38 league games, Martinez's men are a point ahead of the Reds and five behind leaders Arsenal.
At the very least, Champions League qualification looks a realistic prospect for Everton, but the Spaniard remains reluctant to speculate how things will end up.
Giving his thoughts on how they are faring, Martinez said: "I think we can improve.
"(Their current tally of) 37 points is an outstanding return halfway through the season, and looking back, we have had two defeats, and probably of the (seven) draws, there have been more unfair than lucky ones.
"But I think there is room for improvement and that is the target we have from now until the end of the season.
"We have the majority of the top sides coming to Goodison and it will be a great challenge to fulfil our potential - I don't think we have done that yet."
Asked if he thought securing a top-four berth - and, thus, a route into the Champions League - was possible, he added: "You will always hear me saying it is impossible to set a target in December.
"All we are doing is taking it game by game, and we are quite happy now with where we are.
"We are just trying to get as many points as we can before we go into the final third of the competition.
"If we go into it with options to get into the top four, that is what we will look to do.
"If it is another aim, we will try to finish as strong as we can."
Seamus Coleman put Everton ahead in the ninth minute, bursting into the box and unleashing a powerful shot into the net.
Southampton substitute Gaston Ramirez equalised in the 71st when he beat Joel Robles, who was making his first Toffees Premier League start - and it appeared should have done better in his attempt to save the effort, with a strike from distance.
Three minutes later, Romelu Lukaku fired in the winner - his first goal in six games - by converting from James McCarthy's pass.
Southampton boss Mauricio Pochettino, whose side remain ninth, felt the visitors had been unfortunate to end up empty-handed.
''I thought overall it was a very good game, with both teams going forward and playing good, attacking football,'' Pochettino said.
''But it is a shame, because we leave with nothing and I think we deserved a lot more from this game."