Dundee manager John Brown admitted that his side did not deserve anything from their trip to Hibernian.
Brown's men were already assured of finishing bottom of the Clydesdale Bank Premier League table and could not end on a high, despite a fine display from goalkeeper Steve Simonsen.
Cup finalists Hibs created far more chances than their guests but Simonsen managed to keep them at bay until 11 minutes from time, when he was beaten by a fine header from David Wotherspoon.
And Brown said: "Full credit to Hibs, they were by far the better side. Our goalkeeper kept the score down.
"We have put in a good shift but the quality wasn't there, we never really created anything.
"Hibs have got everything to play for, all the players are competing for cup final slots."
Dundee may yet escape relegation, because Hearts could be deducted 18 points on Monday after their majority shareholders UBIG became insolvent.
But Brown said: "As it stands, we are in the SFL and preparing for that.
"We will let the authorities deal with anything else."