The Reds dominated possession against Louis van Gaal's men and saw just one shot on target made against them.
That shot, however, ended up with Wayne Rooney hitting the back of the net. Liverpool had no one of their own to conjure such moments.
But Klopp was pleased with Firmino's contribution up front, with the Brazilian playing as a false nine.
JK: "Firmino again made a really good game. He's a really good centre-forward when he plays there." #LFC— Liverpool FC (@LFC) January 17, 2016
That said, the German was under no illusions about what unfolded at Anfield and admitted Liverpool did not fulfill the one duty required during such a big occasion.
Liverpool pretty much did everything else. They were solid in midfield, won all their tackles and produced some brilliant build-up play.
In the final third, though, they just weren't up to it - while their defending for Manchester United's winner was, as ever from set-pieces, truly woeful.
JK: "It's a derby and in a derby you have one job to do - that's to win." #LFC— Liverpool FC (@LFC) January 17, 2016
Next up for Liverpool is an FA Cup replay against Exeter City, before a trip to Norwich City and then the all-important Capital One Cup semi-final second leg against Stoke City. It's looking like the cups will be all the Reds have to play for this season.