Klopp doesn't ask for more output though unless there are no other options. We've seen this version of LFC now for 9-10 months and it works amazingly well most of the time while usually including no offensively minded midfielders. Fabinho, Gini and Henderson get the majority of minutes now and didn't average a shot or shot assisted a game for the whole season last year. They're well on their way to replicating it again this season.
You're absolutely right - but today there were no other options - both fullbacks were playing conservative for large parts of the game, and so we needed to create openings from other positions. We had 61% possession, so if the fullbacks (our main source of final balls) get jammed up, the midfielders have to pick up the slack, otherwise we're left with launching long balls into the box or hoping for a bit of individual magic - and Firmino wasn't in that kind of form today.
Though it did take Milner tailing off and Keita getting hurt for this style to become the norm. I still think the Spurs away game at Wembley was the one of the best games we played in the last 18 months regardless of score line and it was with a midfield of Milner, Gini and Keita. Maybe it can change again. Guess we'll see.
Edit: Also think 10 total shots when trailing for 60 minutes of the game is almost criminally bad offensive output so the focus shouldn't be solely on the midfield.
You're right that we should look elsewhere, and in that case, we should probably look at both Mane and Origi, who didn't have a shot on goal between them all game (although Origi had a blocked shot). And while Mane at least tried to create something, Origi contributed nothing impactful to the attack, and spent most of his time doubling up with Robertson or moving the ball for possession.
Almost all of his successful passes and crosses were backwards and short, and none into the box to create danger. It was a waste of an attacker in a big game. Was it tactical, or did he just play that way of his own volition? Only Klopp and he knows. But it unbalanced our attack for sure.
We were essentially playing against 12 players given Atkinson's/VAR's apparent bias, so we really needed to do something more with all of our possession. If our main avenues of attack were being dealt with, we had to find something different to take advantage of the spaces left (either the midfield, or a change of formation to release the fullbacks, or maybe using one of the two central defenders more, bringing the ball into midfield and creating overloads that way). United's plan to defend, defend, and defend again worked well for them. They gave us the ball, and we really didn't know what to do with it. It's a problem we've had before.