If the quality of the football is not what we should judge the manager on, it should be his results.
I would strongly argue that Puel and Shakespeare have had sufficient 'tools' at their disposal to finish 7th this season. We have a large squad with proven quality and depth. We pay the 7th highest wages, etc, etc.
Shakespeare had 21 league games, and averaged 1.38 points per game. Over an entire season, this would have given us 52 points. Quite rightly, this was not deemed to be good enough.
Puel has had 23 league games, and has averaged 1.48 points per game. Over a season, this would give us 56 points. However, this includes a very strong start. His last 15 games have returned 17 points (1.13 per game).
Puel averaged 1.21 points per game last season at Southampton (they got 46 points).
Over the last four seasons, the average points required for 7th place is 62 (1.63 per game). Given their comments and actions, I think it's fair to say that this sort of return is the owners minimum expectation.
In pure points terms, he's got to get a minimum of 10 points from the last 6 games to have any argument that he merits a chance to start next season in charge. To deliver the 1.63 over 29 games, he needs to pick up 13 points out of 18.
My guess is that Puel will finish the season with stats no better than Shakespeare had. If so, I cannot see any chance that he'll survive.