Martinez expects to be without Darron Gibson and Arouna Kone for the remainder of the season while Leighton Baines faces around a month on the sidelines with an ankle injury.
When the window opens in January, Martinez hopes to make signings, provided they are of the calibre to improve the squad.
"We are going to use the window to try help the team because we lost two players for the long-term," Martinez explained, although he remained coy on naming specific targets.
"We'll try to see if we can identify one or two players to help the group (but) unless they are out of contract, we will never mention other players.
"It's not going to be just anyone. It has to be a specific personality who has the quality to help the team."
Following their 1-0 win over Manchester United on Wednesday, Everton are now unbeaten in seven Premier League matches and sit fifth in the table.
Martinez does not want to calm expectations however, instead stating that ambition within the club should be encouraged.
"I think we want those expectations, the tradition of our football club has to be used," he added.
"Financially, we are not fighting with (some) budgets that are in this league but that pushes you to be creative.
"Sometimes you need time to find those solutions but I want Everton to have expectations of winning games and doing well.
"Everyone is aware it is a tough, tough ask to compete wtih some of the big spenders of the league.
"We are excited about fulfiling (our) potential and that's all matters."
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