The Merseyside club are just four points above the relegation zone in 12th place, having won only five Premier League matches this season.
Eto'o this week ended his short stay at Goodison Park by joining Sampdoria, but Martinez believes Arouna Kone can fill the void left by the former Cameroon captain's move to Italy.
The Spaniard has not ruled out delving into the transfer market before Monday's deadline, but will not sign players for the sake of it.
He told the club's official webite: "January is not the place to find solutions (in the transfer market). Our moment of form, we want to change, but the solutions are in the squad.
"There are players coming back from injury to create the competition in the squad and I don’t feel it is the window to bring solutions for us.
"With Arouna Kone being fully fit, I see him as a replacement for Samuel's position and it is more about trying to get the players back from injury.
"Steven Pienaar and Leon Osman have been two players missing throughout the season which has been disappointing because they are important in the way we want to play.
"Leon played in every single game last season and we miss what he brings. So I am looking around that.
"We are always working and if we can do something to help the players we have got at the club then we will do something. But what's clear is that January is not very straightforward.
"You never get value for money (in January), first and foremost, and you will not get players you have been following for a long time. And if you want to rely on January to find solutions for your season then it is a big gamble. But we will carry on working."
