It is an exaggeration to say we pinned them back once Arthur came back. They were pretty relaxed and largely in command at that point. They still had the better chances to add the next goal--by far.
You still have to be able to disrupt the opponent with the ball--and the difference was stark in effort or conditioning. It is not like Gini, Henderson, Fabinho and most others on the pitch (except Mane, TAA, & VVD) were pace merchants. But they were much more organized and were far more disruptive. We don't have to replicate Klopp or Pep ball, but we do need more athleticism than was on the pitch, a higher workrate and more cohesion.
The point is you have to notice the pattern of how momentum is dependent on who's half the game is being played in, and which team is on the back foot. Liverpool swarmed the hell out of us so that the game was being played in our half a vast majority of the time, and when we did have the ball we didn't have players to drop back and carry it forward beating their press. Literally only Busquets did this and he gassed out and became way less effective in the 2nd half.
We won more tackles and interceptions than them, but because we didn't have a system to beat their press we couldn't counteract it and play the game we wanted to. Running more and winning more duels really wouldn't have saved us.
When Arthur came on we were incredibly demoralized and disorganized, but his influence made it so that we could get forward and shift it to putting them on the back foot. When we did that their "numeric" superiority was negated and whenever they won the ball we'd have an easier time of recovering it and continuing our momentum.
I'm not downplaying the importance of having athleticism/running/pressure, but that is not the KEY factor that we lacked which led to us being overwhelmed. It is that we couldn't beat their press because neither Rakitic nor Vidal made ANY effort to drop back, pick the ball up, turn and negate their pressure. That is mostly because they are nowhere near comfortable enough on the ball to do so. We couldn't build out of the back, and we couldn't transition the game to where we wanted it to be.
If we had done that, it would make life SO much easier for our midfielders and defenders.
-It'd be easier to win duels because we'd be on the front foot
-They wouldn't be able to simply overwhelm us by charging at us with greater numbers because their players would be farther back
-They'd get more tired/exhausted while we would save much more energy
-Our structure/organization would play more to our advantage and they would lose their offensive shape
Arthur and FDJ are no defensive slouches anyhow and FDJ is proving to be elite in this regard and shows incredible stamina.
You counteract pressure by beating the press, and that allows you to move the game into their territory. Once you're there, your own pressure is what allows you to keep it there and keep them playing reactively. It's not a matter of pressure vs pressure and who wins more duels. It's pressure vs press resistance and then vice versa on the other end. That's why I'm saying you guys need to reframe how you think about it, and that's why Arthur is so invaluable and his supposed workrate/stamina issues aren't as big as they're made out to be.