Martinez has lost Ross Barkley for five weeks with a knee injury, while Bryan Oviedo and striker Arouna Kone are also on the sidelines with a broken leg and knee injury respectively.
Gareth Barry, Romelu Lukaku, Muhamed Besic and Christian Atsu have all joined to boost the Everton squad but Martinez is not ruling out further arrivals this month.
He said: "Bryan and Arouna are progressing really well and can be involved in group sessions, but from that to playing in a competitive game is a gap that will be very difficult for us to answer, unless we get a lot of attention on day-to-day work.
"We have got a bit of time but over the next two weeks we need to take that into consideration, bearing in mind the transfer window will close."
Everton have been linked with former Chelsea striker Samuel Eto'o but the Spaniard remained coy when questioned on a move for the 33-year-old free agent.
He said: "There are going to be many links - there is still a long time in the window."
Martinez, who guided the club to fifth in the league last season, wants to measure the strength of his side against the title challengers in upcoming games against Arsenal and Chelsea
He said: "I am pleased we are playing two of the best teams in the league before the window closes. That is going to give us a real opportunity to see if we have to do anything or help the players we have at the club.
"But at the moment I am very pleased with the players we have and the squad we have. Now it is just a matter of pushing it and trying to get the best out of what we have got."