The Reds found themselves on the receiving end of 22 Lions shots during the 90 minutes at the City Ground on Friday, but only five of those were on target.
Warburton told BBC Sport after the game: "Millwall were very good. They deserved something from the game.
"They were direct, they were effective. They won the first ball and created chances. Too many times we were loose in possession.
"To play like that and get three points, we are very relieved. We had some good points but were way below our normal level."
In the other Championship game of the night, Sunderland were held to a 1-1 home draw against Derby County.