The European champions were out of sight by half time at Anfield, clocking up a 3-0 advantage which the Reds could not overturn.
Despite this, Rodgers insists that he cannot fault his squad, who simply came up against an "outstanding" Madrid side.
"You'd see lots of teams maybe crumble at 3-0 down against a very good team with speed on the counter, but I was proud of my players, in a young team, with the way they kept going," he is quoted as saying by FIFA.com.
"I thought they were outstanding. They've got many players with big-game experience and quality right through the group.
"In the first part of the game we looked a threat, but the first goal knocked us back a bit and very quickly we conceded two poor goals. They played very well. The quality and speed of their game is at a high level."
Liverpool are currently third in Group B, level on points with Ludogorets Razgrad who occupy second place.