Mark McGhee insists Dundee’s relegation fate is still to be decided.
The rock-bottom Dark Blues remain five points adrift of 11th-placed St Johnstone after the two teams drew 1-1 at Dens Park.
Jordan Marshall opened the scoring for the home side but Shaun Rooney salvaged a point for Saints in the second half.
With just four games of the regular season left, Dundee look to be on the brink of being relegated straight back to the Championship.
But manager McGhee, who has yet to taste victory after 10 games in charge, is adamant no-one at the club will be giving up hope until it is mathematically impossible to stay up.
The 64-year-old said: “The result was fair. The first goal was everything I’d seen in training and everything I had hoped for.
“I thought we would kick on from that and that this would be the day to get the win. In the second half, we weren’t able to do that.
“The one thing I am saying is that we are not conceding.
“We can win a game. If we win next week, then who knows? Maybe we can win another.
“We will keep going until it’s mathematically impossible for us to get the points we need.
“The players have got Monday off and I’ve told them to come back ready to prepare for Aberdeen in the same way.
“You saw how they prepared as they came out the traps really well.”
Meanwhile, despite coming from behind to maintain their five-point cushion over Dundee, St Johnstone boss Callum Davidson batted back a suggestion that the result gave him some comfort.
Davidson said: “No! But we are five points behind St Mirren and Aberdeen as well, so it’s a huge game next week. I think we need to take each game as it comes.
“You saw Dundee fighting for their lives and we are fighting for our lives, as we have done since January.
“We need more of that, especially from the middle part of the game. I want that courage to go and play, not just go long and fight for second balls.
“At times, yes, go forward, but try and play in good areas and get chances. Hopefully we can do that in the coming games.
“I also thought the travelling support were very noisy and a big thanks to them.
“They helped us get the point.”
