The problem is there's only so much a coach can do. A clever system can only go so far when you have a limited amount of talent, he's improved players but there are limits to what he is capable of, and we're seeing him hit that ceiling with us. Klopp hit it as well, he wouldn't be going any further had the club not invested in some genuine quality players to improve the team, and he's generally accepted as a world class coach. He couldn't make Lovren not make mistakes though, or turn Karius in to a world class keeper .. he had to go out and spend massive amount of money to bring in the level of player he needed.
Pochettino didn't get much wrong against Liverpool. The team setup allowed us to compete well, create chances, all that jazz. He made adjustments in the second half tactically and it paid off, but that's all he can do as a coach. What can he do when Trippier allows one of the best crossers in the league 5 minutes to pick out Firmino? Or when Sissoko, clean through on goal, blazes it miles wide? And then his keeper goes and gives away the second goal.
Some will say 'well he signed Trippier and Sissoko, his fault' but you're inevitably not going to get top tier talent most of the time when you're signing players who wouldn't look out of place joining Everton. Expecting him to do much more than compete for top four when Guardiola and Klopp are the top two managers with far bigger budgets is more than a little bit harsh. We barely finished ahead of Liverpool last season and then they went and chucked 140m or whatever at players.
Like I've said before, I'm not entirely happy with him this season, in particular his comments in the press, but if we do manage top four that'll basically be job well done and a good season for the club. If we finish sixth it'll be a poor season but still not exactly embarrassing or woeful considering the squads Chelsea and United have, it'll just be disappointing, especially since we had a huge point gap.
Bottom line is he needs better players, the same ones have let us down over and over again this season and again, there's not much a coach can do about that when he has his hands tied when it comes to transfers. He's tried out pretty much every option he has at his disposal and it's time for the board to back their manager.