The Ivory Coast international's participation in the remainder of the season has been thrown into doubt by an operation on a cartilage problem.
While on-loan Chelsea forward Romelu Lukaku is fit and firing Martinez will not have a problem and despite back-up option Nikica Jelavic having scored just once in the league since December 9, the Toffees boss does not fear problems further down the line.
"It is a big blow (losing Kone). When he came on against Hull (his last appearances) I felt we had Arouna back," he said.
"He then had a nasty challenge and it never settled down. It's going to be a lengthy spell.
"Darron Gibson has been in a similar situation (having had cruciate knee ligament surgery) and those two players are working hand in hand to get back.
"But we have many more options up front.
Martinez denied Jelavic, whose last goal in any capacity for the club was in March in the 2-0 win at home to Manchester City, is suffering from a lack of confidence.
"Niki started the season working hard and scored a few important goals in pre-season and has been working really well," said the manager.
"When he came on on Sunday he looked sharp, lively and full of energy and I have no doubt he will have a massive role and is a very important player for us.
"He is such an experienced player he knows what he needs to do. As a striker you are always going to be in good moments and that happens after scoring goals and you feel you are really effective in the final third.
"He has never suffered a lack of confidence. He is experienced enough to understand we have Romelu in a very good moment of form.
"Niki is not suffering at all, he is fighting and waiting for his opportunity.
"It is good to have that healthy competition. You see how Romelu has been performing and that is because people have been setting the same high standards in training."
Martinez insists the long-term injuries to Kone and Gibson have not altered his thinking as the January transfer window approaches.
"We will use the next six, seven, eight weeks to get a clear assessment of the squad and see how the youngsters are developing because it is important to give them an opportunity," he added.
"Every window we are working hard to make sure we are helping the squad.
"It is not a case of bringing in players for the sake of it in every window, it is the opposite.
"It is trying to identify characters and personalities who can fit in and help the squad if there is any need.
"That will always be the case, with injuries or without injuries."
Everton head to bottom-of-the-table Crystal Palace on Saturday looking to ensure they keep pace with the six sides currently above them.
Martinez believes the Londoner's paltry points haul of three from 10 matches is not a true reflection of their quality.
"We will never take any game lightly. Palace have been unfortunate in terms of results, they have been in games more," he said.
"When you get promoted you are either in that honeymoon period when everything goes in your favour and you develop momentum or it is the opposite and things don't go your way and the confidence and belief you had in that successful season which got you promoted is not there.
"They are much better than the points reflect in the table. At any time they could click into place and the last thing we want is for that to happen on Saturday."
- Sports & Recreation
- Romelu Lukaku
- Nikica Jelavic
- Darron Gibson