The Jambos are currently 20 points behind the remainder of the Scottish Premiership following their 15-point deduction for falling into administration prior to the 2013/14 season.
With a drop to League One looking highly likely, midfielder Stevenson is bracing himself for the worst but insisting that the Edinburgh club will give their all in their remaining fixtures this term.
He also admits he has given no thought to the fact that Hearts could be sent down if they lost to Edinburgh rivals Hibernian at the end of March.
"I haven't even thought of that, to be honest," he said in the wake of the weekend's 4-2 loss at Kilmarnock.
"If it is going to happen it is going to happen. The biggest thing for us as players is that we don't go down and just accept it.
"For everything the club has been through it would be poor from us to do that. I know, as one of the most experienced players, that that won't be happening.
"We have nine games left and the least the club and the fans deserve is that we give 110 per cent in those games."
Hearts have won five matches, drawn six and lost 18 this season and have a goal difference of minus 29 to be condemned to the foot of the Scottish top flight.
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