The defender's poor back-pass was intercepted by Rodrigo Pinho, who beat Benfica goalkeeper Odisseas Vlachodimos.
Benfica went on to the win the game 2-1 but after the encounter, Otamendi wrote: "Sorry and thanks are the words I take at the end of this game.
"I'm sorry to all Benfica fans for this start and thank you ... thanks to my teammates who are always with me and who supported me from the first to the last minute. I will work even harder to improve."
After five seasons at City where he also made a number of individual mistakes, Otamendi moved to Benfica in a €15 million transfer deal in September and signed a three-year contract.
Otamendi promised to "bring experience and help Benfica grow" during his unveiling. However, he endured a nightmare start when he gifted two goals and conceded a penalty on his debut in Benfica's 3-2 league win over Farense on Oct. 4.
Benfica coach Jorge Jesus said he has full confidence in the veteran centre-back.
"It's true that it [Maritimo's goal] was an individual error but that's part of the game," he said. "It's true that we can't commit this type of mistake. But this is part of their profession. My confidence in him is the same as when we went acquired him."