Since losing to Liverpool on the opening day of the campaign, Arsenal have drawn with Leicester City and secured wins over Watford, Southampton and Hull City.
"He's shown he's a great manager and I think he's been restricted a bit on the financial side in the past," Ljungberg told Sky Sports News. "They were second last year and this year hopefully we can win it.
"I think some people wanted some signings in the summer but everyone knows English clubs have a lot of money at the moment and if you ask for a player they raise the prices. He managed to get the players in the end."
Arsenal's next game is against Chelsea at the Emirates on Saturday.