Liverpool destroyed their opponents in every area except scoreline.
Sam Vokes and Andre Gray netted first-half goals for the Clarets at Turf Moor as Liverpool failed to build on their 4-3 win at Arsenal last weekend.
It was something of a freak result under the circumstances.
Jurgen Klopp's men finished the clash with 81% possession and no fewer than 26 efforts at Tom Heaton's goal, though only five of those were on target.
And Nevin says it was amazing for Burnley to hold out despite the constant pressure.
"For the away team here to be 2-0 down given the possession they've had it's just incredible," he said to BBC Sport.
Liverpool simply did not do enough on the day, despite what the statistics suggest. They had very few goalscoring chances and it is a big concern.
Sean Dyche's side stood up to the task and earned a very hard-fought three points which Liverpool fans can't really argue with.
The only bright aspect of the Reds' performance was their luminous green attire. Aside from that, it was quite abject and perhaps their win at Arsenal was a bigger reflection on the Gunners than them, on the day.