Despite the Dutchman's 26 goals helping Sir Alex Ferguson's men reclaim the title, the England star thinks his teammates were too reliant on Van Persie last season.
Oxlade-Chamberlain, 19, said: "It is always going to be a blow when you lose someone like Robin, who is a world class striker.
"But from a team point of view, it has helped us massively because no team is about one player. This season we have had to find goals from other areas on the pitch.
"A lot of players have had to step up and take the bull by the horns. I think Theo Walcott really stepped up and proved himself with his goals."