It's an interesting way to win a game - I think it's harsh to say that Burnley scraped it.
Liverpool have sufficient attacking firepower to blow away most teams who come at them with similar attacking intent. Burnley simply played to their strengths by ceding possession and then exploiting the slightly wobbly Liverpool defence twice over before shutting up shop.
Some call this anti-football which imo is rollocks. Sure we all like to see fast attacking and free flowing football but there's more than one way to skin a cat.
Mind you - I can get hypocritical about this when teams do it to Chelsea.

Although to be fair (certainly both times under Jose) there were spells in our recent history when you'd be pushed to find a better cede possession/fast counter team in Europe.