Speaking to Marketing after his keynote speech at Facebook's first Marketing Conference in London on Tuesday (28 March), Bosworth said: "It has to be a long term play. You can't just make the number of fans go up to win."
Bosworth said brands "have to be much better at producing good content" to get noticed on the site and compete with messages from users' friends and family, citing Burberry and adidas Originals as good expamples of brands doing this well.
In TV advertsing, he added, brands also now have to compete harder to catch viewers' attention.
Bosworth said: "It used to be with TV you could buy a captive audience, but now people can tune out more easily […] you have lost that captive audience and you have to compete."
At the event's press conference with David Fischer, vice president of business and marketing partnerships at Facebook and Joanna Shields, vice president and managing director of Facebook, EMEA, the issue of fan numbers was also raised.
Fischer was asked about comments made by Diageo's Phillip Gladman at last week's ISBA conference, where the marketer said brands should abandon social networks if they are unable to build communities of a million consumers. Fischer replied: "There is no prize for having the most fans [but] fan acquisition is important".
He said Facebook does not put a number on expected fan acquisition, as this number depends on the type of business and customer base, but stressed that brands should adopt the "always on" approach and ensure they have a "sustained relationship" with fans.
Shields agreed, adding, "engaged fans are as important as numbers".
The event was the first of its kind for Facebook in the UK and attracted around 500 marketers and agencies.
Follow Sarah Shearman on Twitter @Shearmans