Burnley pushed Klopp’s side all the way after taking the lead and although the 3-1 scoreline made it look emphatic, only a world-class save from Alisson at the death stopped Burnley equalising.
Alisson also started a counter-attack following the save that saw Xherdan Shaqiri score Liverpool’s third goal that finally made the game safe.
Talking on Match of the Day (BBC 1, Wednesday 1045pm), Mills singled out the two Liverpool players for praise saying that they meant Liverpool didn’t have to play well to win.
“Van Dijk and Alisson have made all the difference this season and Liverpool don’t have to play that well to win matches anymore, and that’s a big plus,” Mills said.
“All the best teams have that spine of wonderful players and for me those two are incredible footballers who have made a brilliant difference.”
It’s hard to argue with this assessment. Alisson has already paid back his huge transfer fee and we’d estimate he’s worth between 10 and 15 points a season on his own for Liverpool. Virgil van Dijk is probably the best centre-back in the world at the moment and his assist for the second Liverpool goal was fantastic on Wednesday night. Together they’re incredible and Mills is right – they’ve made a massive difference for Liverpool. And you can overstate the importance. They might have scored three goals tonight but their attack hasn’t been firing on all cylinders this season and the defence is what’s stopping them from dropping points against the sort of teams they were drawing with and losing to before Alisson and van Dijk turned up. It’s the difference between being legitimate title contenders and also-rans. It might be tough to keep pace with Man City this season, but Liverpool are giving it a damn good shot.