The 30-year-old has been consistently finding himself playing out of position under Klopp, particularly in a left-back role, despite operating for most of his career as a midfielder.
However, Buck claims that Milner respects Klopp and is ready to sacrifice himself for the greater good of the team.
"James would say he's gone from one world class manager to another. He has huge respect for Jurgen. He's 30 but always learning and embracing things," Buck told the 5Times podcast.
"Left-back is a difficult one for him as he's naturally right footed. I wouldn't say he finds it easy but as people know from his personality and temperament he will always put the team first.
"James wants to contribute to the team and will sacrifice himself in order to give the team the best opportunity to win, It's a fluid system.
"He got a couple of assists against Burton as he got forward a lot and overlapped. It was the same at Tottenham.
"But you still have to have that discipline to fill in and cover defensively. He's learning all the time.
"With no European football or international football, he's extremely focused on doing the best he can for Liverpool."