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."