Gallas, who had earlier scored an own goal, grabbed an injury-time equaliser as the leaders denied United top spot in the Barclays Premier League at the Emirates Stadium.
Gallas hailed his side's teamwork and told Sky Sports: "We had to fight. We said if we had to die we would die together on that field.
"In the first half we tried to play football but it was not really easy.
"We played very tight. It was difficult for us to find good space.
"We conceded a goal - maybe I was a little too late but that is football.
"In the second half when we came back on the pitch we said we had to play better."
Arsenal, with a game in hand, remain unbeaten and top of the table from United only on goals scored.
Gallas added: "I think we had to stay top of the table, we have to put pressure on other teams - other teams can go back like Chelsea or another team.
"We have to stay at the top to put pressure on Manchester United and maybe they can make the mistake."