Touched on this sort of thing before. Klopp's done very well to get Liverpool back in the conversation again. You only have to go back 5 or so years and they're basically a mid-table team. They weren't anywhere near United, Chelsea, Liverpool, Arsenal, City or Spurs until a couple of seasons ago.
However, comparing Liverpool to Burnley is pointless. Burnley aren't expected to win anything. Liverpool are. There's a fundamental difference between the two clubs. Success for Liverpool is challenging for and winning silverware. Success for Burnley is not measured in the same way, and survival in the Premier League would be seen as a success for them, never mind qualifying for Europe.
I agree to an extent that success can not only be measured in trophies, and I think you'd be hard pressed to find a Liverpool fan that doesn't think they're still in the ascension. The point is fast approaching though where they will have to win something of significance to make that next step under Klopp, attractive football or not. It's the main criticism aimed at Spurs under Poch, was the same criticism aimed at Wenger's Arsenal, and is already a criticism being aimed at Mourinho (alongside criticisms of the style of football).
Klopp getting Liverpool into regular top 4 contenders, perhaps occasional title contenders, and maybe reaching a cup final every few seasons, is obviously an improvement from the 7th-8th placed finishes and maybe a Europa League appearance they had before he got there. But if in five years Liverpool under Klopp are without a trophy, where does he stand then? What happens if he leaves, and they suddenly plummet back to 6th/7th in the table? There's no lasting legacy and no silverware to show for anything.