So what can Levein do to get these fans back onside and ensure his remaining time in the job isn't shrouded in negativity?
After Saturday's loss, the main thing that stands out is the head-scratching starting XIs. For two weeks in a row Hearts fans have been perplexed by the way the team has shaped up and it certainly hasn't translated to success on the pitch as they looked to capitalise on the back-to-back victories over Hibs and Aberdeen.
Against St Mirren there were two full-backs in a back three, with two wingers at wing-back, in a 3-5-1-1. This was followed by the same system being used against Kilmarnock, but with no attacking midfielder in the central midfield three and two midfielders playing up front together.
Levein has pointed to chances missed in both matches and it's certainly true that neither performance was quite as listless as the Ross County encounter earlier in the campaign. But Hearts didn't look like dominating either game. Even with the injuries the squad has had to contend with, there is still enough quality in the team for them to be performing much better than they are.
Arguably the most important positions in a 3-5-2 or 3-4-3 are the wing backs. They have to contribute positively at both ends of the park. There needs to be defensive discipline, bags of energy and the ability to make things happen in the final third. As it stands, Hearts don't appear to have those players at present. Jake Mulraney is lacking on the defensive side (just see Kilmarnock's goal on Saturday for evidence), while Michael Smith, though he does his best, doesn't quite have the attacking arsenal to be a consistent menace in the final third. Aaron Hickey is probably the stand-out candidate, but he's still just 17 years old and playing in his first full season as a professional.
In order to facilitate the system on Saturday there were at least four players operating in an area outwith their comfort zone: Hickey at right-wing-back, Smith at centre-back, Mulraney at left-wing-back and Ryo Meshino up front. That's without including Christophe Berra and whether he is at his best playing on the left of a back three (he isn't) or Sean Clare as a No.10 without a striker in front of him who can effectively hold up play.
Over the course of 2019 there have probably been five matches where they've played well from start to finish: back-to-back victories against St Johnstone and Kilmarnock in January, Hibs at home in early April and Celtic in the Scottish Cup final (two games they lost, funnily enough) and the Betfred Cup triumph over Motherwell in August. They've played well in spells against other sides - typically against Aberdeen - but haven't managed to put it together for 90 minutes.
The St Johnstone and Killie wins came using the 3-4-3 system and there's a chance it's clouded Levein's judgement on the matter for the rest of the year, because Hearts have rarely looked good in the formation since then. The Hibs, Celtic and Motherwell matches all saw Hearts adopted a variation of a flat-back-four system. Even the recent victory at Easter Road was achieved by a change in the system as Levein introduced Callumn Morrison to Sean Clare and moved from a 3-4-3 to a 4-2-3-1.
The latter is a system that, on paper at least, seems to fit what's left of this injury-plagued squad. It allows Meshino to operate in his best position, which is essential at the moment because he's the most threatening attacker. It bolsters the defence by not only allowing Smith and Hickey to play in their natural roles, it also provides protection to the injury-depleted centre-back corps without sacrificing much in the way of attacking intent.
Of course, the manager can only do so much and the players need to take their share of the responsibility also. The defence has been incredibly leaky all season with individual mistakes being the main reason behind the majority of those conceded, while some of the attacking players also have to face up to the pressure on their shoulders also.
But it's the manager's job to put the players in the best possible situation in order to do that. For the team being, that ideal situation does not involve wing-backs.