The second-placed South Yorkshire club suffered a setback to their title aspirations on Thursday night in Scotland when they dropped a point in a 4-3 overtime defeat against the Braehead Clan.
They now sit seven points behind leaders Belfast Giants with two games in hand and a double header to come next weekend between the top two in Northern Ireland.
It means, mathematically at least, the Steelers still control their own destiny but they head into a home double header this weekend knowing any further slip-ups will probably end their title hopes. Effectively, every game is a game seven.
There will be an early chance for revenge when Braehead visit the Motorpoint Arena on Saturday night (7pm) before fourth-placed Cardiff Devils arrive on Sunday (5pm).
Four points are a must for the home side as Belfast are expected to take a maximum haul when they begin their last five games this weekend with a double header at Edinburgh Capitals, whose 6-2 win over Dundee was their first victory in 15 games.
“We don’t have anywhere to run anymore,” said Finnerty, who also confirmed key British forward Ashley Tait will sit out the rest of the season with an ankle injury.
The last two summers have been periods of turmoil for the Steelers, with financial problems prompting changes of ownership and leaving the club shrouded in uncertainty. But, under current owner Tony Smith, Finnerty believes a repeat of those difficult times is unlikely in the foreseeable future.
“We won’t give up on this title but, regardless of what happens, I think it’s clear to see that, considering where we were last summer, we’ve laid some big foundations since then to ensure a good future for the club.
“We’ve made some huge steps both on the ice and, perhaps more importantly, off the ice. The fact we are still in a position to be challenging for the title is impressive.
“We’re certainly not out of it, but you’ve got to fancy Belfast to take four points in Edinburgh. We can’t afford any more slip-ups or we’ll be out of it. We need to go to Belfast still in the race and we’re going to have to win twice in regulation there which will be a tough ask.
“I still believe in this group of guys, but it’s amazing how fast some people turn on a team when they lose a few points, but I guess that’s the same in all sport.”
Defenceman Rod Sarich, who made a successful return to the ice last weekend in a 3-2 shoot-out loss to Belfast, said the Steelers needed to avoid a similar slow start to the one they had in Braehead on Thursday.
“A couple of big decisions went against us on Thursday - their third goal was kicked in and then we thought we had scored on a breakaway - but we played well after getting off to a slow start,” said Sarich.
“We need to make sure we’re ready from the off and make sure we take our chances. Braehead are a very good team with a very strong top line and their power play is good so we know they can hurt us.”