The German international admitted that gaining a man advantage after 20 minutes following Emmanuel Adebayor's red-card challenge on Santi Cazorla was a crucial factor but praised his team's spirit to force the turnaround.
He told the club's official website: "From the very first whistle it was an amazing day, I don't think it could have been any better.
"It is always difficult to play against ten men because they have nothing to lose, but in the end we managed it and it makes me very happy to be successful on a day like this.
"Maybe the sending off was vital today but we will take it. I kept standing in the box when they dropped deep to try and be lucky. The ball in from Theo Walcott was very good and the goal was vital for us."
Victory in the north London derby allowed Arsenal to move ahead of their bitter rivals into sixth place in the Premier League.