The win was Arsenal's first over United in the league since May 2011 and the biggest league win over the opponents for 17 years.
Van Gaal admitted he was 'shocked' by the capitulation, criticising his team for allowing Santi Cazorla and Ozil the freedom to dominate the game in the first half.
"The problems did not start at the back, they started in midfield. The midfielders, especially Cazorla and Ozil, had too much space and they have the quality to make the most of it," the Dutchman said.
"We lost every duel, every second ball. We were not tight on their midfielders, and they can play because they are a fantastic team."
England international Carrick, who was paired alongside Bastian Schweinsteiger in the centre of the park for United, also admitted the performance wasn't good enough.
"We just gave them a bit too much space and they played well and it came off for them," he said, quoted by the club's website (www.manutd.com). "We did too many things wrong... It was certainly a bad day.
"I am hoping it's a one-off, as there's been no sign of that recently.
"It's a setback, but we're still up there and just need to take this one on the chin, take whatever criticism comes our way and come back stronger.
"The last international break came after the Swansea game, so we've just got to go away, refresh and come back stronger again," the 34-year-old added.
United visit Everton when the Premier League resumes on Oct. 17, while Arsenal travel to Premier League new boys Watford.
(Reporting by Simon Jennings in Bengaluru; editing by Sudipto Ganguly)
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