Speaking exclusively to Marketing at the Labour Party Conference, Burnham would not rule out a 9pm watershed ban, but his comments suggested that such action was looking increasingly unlikely.
The culture secretary said research did not prove a link between alcohol ads and underage drinking.
He added: 'Some people forget that it's not like when they were growing up. These days children get messages from lots of places, not just TV.'
Alcohol Concern and children's campaigners are calling for a 9pm watershed ban for alcohol ads, but broadcasters are strongly opposed to the idea.
Earlier this week, Burnham dined with ITV executives including executive chairman Michael Grade. It is understood they expressed serious concerns about further ad restrictions.