"Arsenal kept the ball and had a lot of possession, but they were never really threatening," he said. "Football is about scoring goals and winning games.
"I do not think they had a clear-cut chance created in the first half, apart from the header by Gallas, and that was a set piece.
"Defensively, we did a good job and tried to control their so-called beautiful football.
"They keep the ball and try to play that way, but when a team is as good defensively as ours, you can keep them at bay because we played very tight together."
Hargreaves added: "Both of our goals were from really beautiful pieces of play and theirs were a bit more scrappy."
Ryan Giggs still thinks that the league will be a four team race:
"It is still early yet. The test will be around Christmas time.
"I think it will be ourselves, Arsenal, Chelsea and Liverpool.
"It is whoever can sustain their form throughout the season, can handle the injuries and suspensions the best."