Second-half goals from the ever-impressive Romelu Lukaku and substitute Leon Osman handed the travelling Toffees a 2-0 win at Aston Villa on Saturday, with Tim Howard's excellence between the posts also a decisive factor.
The result left Martinez's men with 15 points from the last 18 available to them and kept them in touching distance of the Barclays Premier League front-runners.
In previous seasons Everton might already have been talked about as potential Champions League gatecrashers but, with the field seemingly more crowded than ever, the Spaniard was content to play down talk of a top-four challenge.
"We're in October. It would be stupid of me to say that," the former Wigan boss said.
"I don't think this was us at our best. If we were our best and the league finished tomorrow we'd have a great chance, but there are many things we need to do better, many things to improve.
"All we want now is to get many points as we can while we're developing and we can use the competition for places here to become as good as we can.
"The nature of the competition is to get as many points as we can then in March or April we can reassess the situation and see where we can fit in to the league at the end of the season."
On-loan Chelsea striker Lukaku was the understandable centre of attention on Saturday, having outperformed his fellow Belgian Christian Benteke and registered his fifth Premier League goal in as many matches for Everton.
But Martinez was also effusive in his praise for Howard.
Had he not made a stunning penalty save from Benteke in the seventh minute and followed up with at least two more crucial interventions, Villa may have been home and dry by half-time.
"I thought it was a very important clean sheet and nobody deserved it more than Tim Howard," Martinez said.
"For the first 25 minutes we have him to thank for being in the game.
"Without Tim it would have been a very difficult second half and it was a great example of how lucky and how privileged we are to have a player like Tim Howard.
"When the team most needed him he kept us in the game and gave us a kick up our backsides."
Villa boss Paul Lambert was forced to reflect on the match from the opposite side of the fence - an opportunity lost after a blistering start failed to yield a goal.
His side have now taken just three points from five games at Villa Park, while collecting seven on the road.
"We seem to be doing it the other way around... going away from home and winning and finding it hard here," he said.
"It's something you've got to overturn. You have to.
"But I can't fault them for giving it a go. They should have won. They've delivered for me more times than not so I can't be critical of them.
"I'm not going to sit here and criticise because they've given everything they've got."
Villa goalkeeper Brad Guzan, who made a fine save of his own off Lukaku with the game goalless, added: "On another day it could have been 3-0 at half-time; done and dusted.
"That's football. You have to be able to take your chances and, unfortunately for us, we came up a bit short."