However, it is hard to see what more the players can do to divert their supporters' attentions from the flux surrounding their club right now.
They were valiant, if limited, in defeat yesterday, twice recovering a deficit only to lose out as a muscular Inverness Caledonian Thistle side plundered three goals from three free headers.
Two of them were planted past Jamie MacDonald by Gary Warren, while the other fell kindly for Billy McKay to nudge over the line. "That's when you miss guys like [Marius] Zaliukas and [Ryan] McGowan; you can't replace guys like that in those situations," said Hearts manager John McGlynn, referencing the injury-enforced absence of his captain and sale of the influential Australian.
Some might argue the presence of Andy Webster, Danny Wilson and Darren Barr would mitigate against those losses, but the latter was especially culpable in the concession of the first goal.
Although Hearts had enjoyed the early territorial supremacy, Inverness's threat, evident both on the break and aerially, took just 16 minutes to bear fruit.
Aaron Doran scampered down the right after a Hearts attack petered out and, although his run was brusquely curtailed by Webster, Warren headed the home from the resultant free-kick with Barr flat-footed.
Inverness's other two goals were acquired equally cheaply. With the scoreline poised at 1-1 and Hearts in the ascendancy after Jason Holt's equaliser, a free-kick from deep by David Raven was directed across goal by Owain Tudur Jones for McKay to bundle in at the back post.
Then, with the hosts having again hauled themselves level again through Webster, Inverness found a winner with 13 minutes remaining. A Graeme Shinnie corner flashed into the area, where Warren was again free to snap a header away from MacDonald's grasp.
"They could have let their heads go down but we showed great character," said Inverness manager Terry Butcher. "We've answered a lot of questions: did we have what it takes to win? We've had a real slump, apparently, and that's us back to second place... wonderful."
Butcher has exchanged barbs with supporters in recent weeks, after a run of six games without a victory since his team's Scottish Communities League Cup semi-final defeat to Hearts, while McGlynn, too, was criticised during the week for questioning the expectations of the Hearts fans.
He is likely to be subject of further derision as his young side – the starting XI had an average age of 22 – continue to labour in 10th place in the SPL. "We have to stick together, but it is a harsh lesson for them," McGlynn said. "We played some good football to get back into the game and showed good spirit, but if you don't defend set-pieces properly..."
McGlynn was right, up to a point. Hearts did funnel the ball around sharply at times but found clear openings hard to fashion, as the creative talents of Holt, Jamie Walker and Arvydas Novikovas were suffocated by the visitors' massed defence.
They were further hampered by the neutering of Michael Ngoo, booked in the opening seconds for laying hands to Warren after a robust early challenge.
Regardless of that, the Liverpool loanee was all too often isolated amid a forest of defenders. With Hearts restricted to hopeful efforts from distance, it is little surprise both their goals came from outside the area. Holt hauled the score back to 1-1 after 55 minutes, darting past a defender at the edge of the box and unleashing a 20-yard drive that flashed past a startled Ryan Esson.
After McKay's 23rd goal of the season put Inverness back in front, a slice of fortune restored parity again. Ngoo rose highest to meet a disputed corner after 74 minutes and, although Nick Ross headed off the line, Webster's rasping return looped wickedly off the advancing midfielder and spun past Esson.
Hearts showed that, for all their off-field woes and inexperience, they possess resolve. What they don't appear to have is the patience of some of their supporters.