After the final whistle, Gallas was the last off the pitch as he celebrated with fans.
The skipper said: "It was really important for us to win against Manchester United, because we want to stay in the race - to do that we want to win every game.
"The last few games we have drawn and lost, so it was important to win at home."
Gunners boss Arsene Wenger felt Gallas was not the only leader he had,
"You need a shared leadership on the pitch - five or six on the pitch," he said. "We had 11 leaders on our side because everyone took initiative at the right time."