Steven Fletcher proved the Black Cats' hero as he struck a decisive double to expose the defensive weaknesses of the Latics, who now sit second from bottom in the Premier League.
After eight years in the top-flight, Martinez insisted his side will galvanise themselves for another relegation battle and are taking nothing for granted.
"We never take anything for granted," the Spaniard said. "If we had done that we would never have had eight seasons at this level.
"Today we weren't good enough defensively for 30 minutes. We need to rectify that. Ivan Ramis' injury last week cost us today's points. That is something I need to correct."
The performance of new boys Roger Espinoza and Angelo Henriquez were positives for Martinez, with Henriquez netting his first goal since a loan switch from Manchester United.
"I was pleased that they didn't seem like new players," said Martinez. "They looked like they knew exactly what they were doing.
"Roger is someone with great energy, which he compliments with a real style in possession. Angelo is a goalscorer and to score a goal on your Premier League debut is a great boost for his career."