It's rarely good to view a game by it's scoreline. You can win 3-1 with very little of the ball, parking the bus and a few set pieces, you can lose 3-1 by having 20 shots and the opposition having 3.
At 0-1 Liverpool let us have the ball and were more than comfortable to press us into mistakes and hit us on the break. Sure, we had more of the ball, but does that mean we were controlling the game if they were letting us? If we were able to take advantage of it and have some impetus then maybe, but since we weren't really able to put this 'control' to any good use, and as soon as it got to a point that Liverpool wanted to stop us coming further then it stopped.
I thought Herrera was pretty mediocre by his own standards, in a premier league game he'd have likely got multiple bookings and a penalty for that performance. He gave the ball away carelessly, and only really showed quality in the ball to Hernandez.
That's where our quality shone through in a burst - a great ball, a great cross, a great finish. We were able to gain some confidence and picked up here, and quickly made it 2-1 with a some good play and a bit of luck.
From then on we managed to control the game for the most part, but we were still allowing Coutinho, Sterling and somewhat Ibe to bypass our midfield and bear down on our defense needlessly. If they'd had Sturridge playing, perhaps they'd have punished us for it.
I'm not saying there were no positives to take from the game, there definitely were.. but the system and players definitely need some time, and there's clearly work to be done. I don't think it should be considered a good performance by our own standards, a good result mind and with some promising signs and courage to take away from it, but plenty to work on also.