Jurgen Klopp’s side ended a 30-year wait to be crowned English champions in June.
Form dipped once the title had been secured, with two of the three league defeats they suffered all season coming in their final seven matches, while their 100 percent home record also fell in a draw against Burnley.
The players are currently on a break before pre-season begins but Milner, who won two titles in three years with Manchester City, says they have to be switched on when they return.
“I think it’s getting that balance right. We have to enjoy it because we know how hard it is to win trophies,” the 34-year-old told liverpoolfc.com.
“We’ve been very good to do it but also lucky to win the amount of trophies we have had this year.
“Trent (Alexander-Arnold) thinks it’s absolutely easy, he just turns up and wins trophies every year but I can assure you, with the amount of years I’ve had in my career, it’s not that easy.”
He warned his teammates against letting their standards drop.
“That would be criminal and something we definitely don’t want to look back at,” he said.
“We have a couple of weeks to enjoy this and enjoy being champions and then, as soon as next season starts, it’s down to the fans to carry on enjoying it and enjoy being champions for us.”