okratis Papastathopoulos and Nicolas Pepe scored in a 2-0 win that lifts Arsenal to 10th in the Premier League, four points behind fifth-placed United.
Arsenal defender David Luiz said his team can "do big things" after beating Manchester United to earn a first win under new boss Mikel Arteta.
"I believe he [Arteta] can improve every player," said 32-year-old Luiz.
"Mikel is a great coach and knows football. He was a great player, he brings things and I believe in his philosophy.
"We are going to do big things in the future, but step by step."
“Of course it’s playing on our decision-making,” Solskjaer said of United’s depleted midfield. “When you’ve got two players out - Paul for a month and Scott for two - that’ll gives us less options and we’ve got loads of games and important games
“But still it’s got to be right and that’s the big point here and if it’s available and possible we’ll do something, yeah, definitely, we’re looking at one or two.”