Their position looks desperate but boss Jim McIntyre has promised so long as there’s a mathematical chance of avoiding relegation, Dundee will be fighting tooth and nail.
The Dark Blues face Hamilton at Dens Park on Saturday – only a win definitely stops them going down then.
And if St Mirren beat Motherwell at Fir Park, even three points would leave them teetering closer to the drop to the Championship.
For the gaffer, though, what happens elsewhere is irrelevant and all that matters to him is his players keep giving their all.
“As I said to you before, we can bemoan mistakes, decision-making at times, but you can’t say the boys are not putting a shift in because they certainly are.
“I felt for them Saturday night, I really did, because they put so much effort into the game at Motherwell.
“To lose it the way we did, in the last minute, I didn’t feel we deserved that.
“Now it’s just a case of getting the heads lifted again and get the proper preparation done for this week.
“We are in last-chance saloon and even that might not be enough, so again, we have to do our bit.”
Jim is not hiding from the fact that after nine defeats in a row, the chances of Dundee staying up are slim at the very best.
He does not believe, however, the end of a five-season stint in the top flight for the club will be the end for him, and he aims to be at the helm next term.
“John Nelms (managing director) and people at the club know what we’ve done behind the scenes and what we’ve had to do in terms of the squad.
“When things are like they were, you’ve got to be brave and make a change and try to improve things.
“Unfortunately for us, results have not matched some of our performances and we’ve not picked up enough points. That’s on me.”
Goalkeeper Jack Hamilton continued his comeback from the broken finger that’s ruled him out since the turn of the year when he turned out for the reserves at Kilmarnock yesterday. The second string went down 2-1 to Killie in what was their final league game of the campaign.