With a League Cup final to look forward to the club hierarchy are unlikely to be swayed by those calls, but they would be wise to heed the growing level of disquiet.
The pressure is now on Hibs, who need to find a way out of their current mess. But doing that will not be easy as suspensions and injuries are again likely to hamper selection when they travel to Paisley on Saturday.
On a disastrous night for the Easter Road club, they not only stumbled to defeat, they saw their backline decimated as Ryan Porteous hobbled off injured and Paul McGinn and Paul Hanlon were both shown red cards for second bookable offences.
One of their games in hand. Hibs had been hoping for three points and the opportunity to propel themselves up the league standings.
Instead, they registered their seventh defeat in nine Premiership games and are still plugged in the bottom six.
The early proceedings action resembled a basketball contest as the play surged from one end to the other, as two teams in desperate need of a victory pressed forward in search of the advantage.
Eleven points off city rivals Hearts, who occupy third place, and lagging behind in the chase for a European spot, Jack Ross’ League Cup finalists are in need of some positive momentum ahead of that Hampden showcase.
Livnsgton, though, are a team with their own concerns. They started the evening second bottom of the table but knew that three points would catapult them up a couple of places and they fought with everything they had to make that happen.
It helped that they were the team to make the breakthrough. It came in the 16th minute when a ball forward picked out former Hibs man Andrew Shinnie as he cut in from the left flank.
Hanlon got across to cover but couldn’t clear the ball far enough and when it dropped, Shinnie fired it across the goal and Jack McMillan was allowed to drill it home, after his markers identified the danger too late.
There was a chance for a quick response when Boyle tumbled in the box. The home crowd fumed as the contact seemed minimal, and he was booed throughout the remainder of the match, but they celebrated when the Aussie forward uncharacteristically failed to convert from the spot, ballooning it over.
It summed up Hibs fortunes at the moment. A player who couldn’t miss earlier in the campaign and has 15 goals already this term, his miss bolstered the home side and left Hibs rattled.
Both managers made changes at half-time, with Scott Allan and Christian Doidge coming on for Hibs but there was still no way back and when both McGinn and Hanlon were sent packing late on, it was a case of trying to hold on as Livinsgton looked to add to their tally.