I take your point and there's no way it's been a consistent issue in every game or even a majority, but I remember watching the Madrid final in particular and thinking it highlighted a struggle to play through the midfield. I think the club saw similar as the Keita deal was completed and we added Fabinho as well - having already brought in Oxlaide-Chamberlain during that season and by all accounts targetted Fekir as well - settlling for Shaqiri instead to play in an advanced midfield type of role.
In the Spurs final I don't recall too many instances of any of the team stringing more than 3 or 4 passes together.
Whether playing through the midfield is something we really target doing is another thing - seems to me most of our build up play in midfield is quick recycling of the ball and ideally getting our fullbacks on it wide who look to link with Bobby or whichever of Mo/Mane they're with. Fabinho and the centre-halves also primarily create triangles with the full backs and when the vertical passes are made, it tends to be in the right/left sided half space for Bobby, or and advanced 8 who's immediately looking to link up with the forwards, or, again (a theme) play the advanced full backs in.
Our style of play is different to cities, and I don't think we put anywhere near as much emphasis on playing through the midfield - we play through our fullbacks much more - and look to get it into advanced areas and the feet of Bobby, Mane and Mo much more regularly. City's game, as an example, or take a Barcelona/CL finalists Madrid - are looking much more to move the ball around more, probing and pulling, looking for a killer pass.
I don't think it's too unreasonable the point that was being made - that our midfield looks a lot better, at least in terms of creativity and penetration when there's that Lallana "type" in it - which I'd add Ox, Keita and, to a lesser extent, Shaqiri too.
The problem with playing through midfield is that you have to play through to someone else at the top of the midfield (usually the attackers). So when we lost our most important one to injury, our midfield patterns of play went right out the window. Depth is super-important to getting the ball from one end of the field to another, and without it, we were always going to be in trouble once Salah went off (him being our "depth" player in possession, more often than not).
It's so much easier to explain in the famous 4v2 "Rondo" exercise -
With the 4v2, all elements of the principles of attack are present - Penetration, Width, Depth, Mobility, Creativity and Surprise. Penetration is the primary objective, Width and Depth give the "shape" (which is the correct use of the phrase "get your shape"), and Mobility/Creativity/Surprise are the technical tools to make the Penetration happen, or to enable Possession when there is no Penetration option.
The aim of the keepaway exercise with 2 or more defenders in the middle is NOT to keep the ball, but to split the defenders with a penetrating pass. If that isn't on, then you keep the ball until you create a gap that you can play the ball through:
So for our midfield, and especially with Mane and Firmino both happy to drop in to the middle to help out or receive the ball, the loss of Salah blunts our midfield play as without the Depth/Penetration option, we end up going more side-to-side, ending up with the fullbacks, who then have nobody to play to, so the ball gets recycled. The obvious alternative to this is to have dribblers in midfield who are happy in 1v1 and 1v2 situations, hence Keita - but we didn't have him at the time. Against most teams, we can deal with this using patience, because we have more quality than most teams. But against a team like Madrid, with no Salah and a concussed goalkeeper, we can be very easily put off our midfield game.
Which is a long-winded way of saying that "midfield ball progression" has two sides to the coin - the midfield side, and the attacker side, because without dribblers, you have to progress TO someone, and if that player isn't there, ball progression through passing alone becomes almost non-existent (see Rodgers without any strikers worth the name).