Saturday's home defeat to Sunderland leaves the Latics languishing in 19th in the Premier League and with Ivan Ramis and Antolin Alcaraz injured they are short of defensive numbers.
"We haven't got a large enough squad to cope with losing players like Ivan Ramis and Antolin Alcaraz. We need to find a solution," said Martinez, quoted in the Daily Mail.
"January is a good moment to rectify that. It is important we bring a defender in, but I don't think we will be looking at the Spanish market this time.
"It is difficult for a foreign player to arrive in January and make an impact, but we do need someone."
That someone could include a trio of reported targets with Wolves man Ronald Zubar, Liverpool player Sebastian Coates and ex-Rangers defender Madjid Bougherra all linked with a move.
Zubar is out of contract in the summer, Coates could be available on loan, while Bougherra might be tempted to return to Britain from Qatari side Lekhwiya.
Whoever Martinez opts to sign will be tasked with bringing greater defensive intensity to the Wigan back line.
"I am concerned about the lack of points. We have been playing much better than that," added Martinez.
"We are not protecting our area well enough. These players can put that right, but I'll take the responsibility.
"I'll set the team out in a certain way, but you still need to be able to defend one-v-ones and have that concentration and defensive intensity."