Martinez's team trail only Aston Villa in the goals against column this season and once again their defensive frailty was exposed after they had taken the lead through James Vaughan's own goal.
Antolin Alcaraz has not made an appearance since August due a calf injury and Wigan's problems have been compounded by the season-ending cruciate ligament rupture suffered by Ramis.
"What is clear is that we weren't strong enough defensively," Martinez told reporters. "If Ramis had been on the pitch it would have been a very different situation.
"I need to make sure we rectify that and bring someone in who will give us the same strength Ivan was giving us."Craig Gardner's penalty and two goals from Steven Fletcher gave Sunderland a commanding lead at the DW Stadium, with Angelo Henriquez's late goal proving only a consolation.
The defeat left the Latics lying in 19th place in the Premier League and four points ahead of bottom club QPR.