The Gunners went ahead through a fluke Cesc Fabregas goal early on, but were put under pressure when Alex Song was dismissed in the 55th minute.
Czech Republic international Rosicky then blundered a chance to put the Gunners 2-0 up at the Stadium of Light when he blazed his spot-kick attempt over the crossbar.
The Black Cats went on to snatch a last-gasp equaliser, causing Arsene Wenger's men to slip four points behind Premier League leaders Chelsea in the standings, and Rosicky admits his penalty gaffe was costly.
When asked whether he and his team-mates discussed the miss in the dressing room after the match, Rosicky told his personal website: "Of course we did.
"We were very disappointed because we could have won. But we made errors for which we paid the full price. I made the biggest one."
Rosicky, who replaced injured midfielder Fabregas in the 29th minute of the clash, assuming the captain's armband, likened his botched spot-kick to his effort for the Czech Republic in a World Cup qualifying match against Holland five years ago.
"Unfortunately, it was nothing new," he said. "I missed a penalty in a World Cup qualifier against Holland in autumn 2005."
The midfielder is not a regular penalty taker for the Gunners, and revealed he stepped up on Saturday because other players were reluctant to.
"Fabregas and (Andrey) Arshavin were not on the pitch at that time," he said.
"Ahead of the kick I communicated with (Samir) Nasri and (Marouane) Chamakh but nobody wanted to take responsibility, so I did."
While admitting the penalty was a crucial moment, Rosicky insists his side should have still managed to take the full three points home.
"In the first half we didn't even have many opportunities," he said.
"Sunderland showed they could frustrate favourites and apart from our partly fortunate goal they did not let us have anything dangerous in front of their goal.
"But after the break we were passing the ball around better and after Song's sending off were the better side.
"Then came the spot-kick, but even without it we should have managed to win. Naturally though, it was the key moment."