Dundee need to take four points from their first two matches after the split if they are to stay in the Scottish Premiership, says striker Kenny Miller.
Jim McIntyre's side are currently three points adrift of St Mirren at the bottom of the division, and a further four behind Hamilton Academical.
They travel to St Johnstone and Motherwell in the next eight days.
"We need four points minimum. If you get that, you go into the Hamilton game with momentum," Miller, 39, said.
"We've been dealt a tough start, with two away games with the teams in seventh and eighth, so we need to get together and scrap and stop giving away silly goals."
Dundee have conceded 16 times during a run of seven consecutive top-flight defeats and have won just one of their last 11 league matches in a run stretching back to the end of January.
The 68 goals they have lost over 33 games is the second worst in the division behind Hamilton.
"In a lot of games, we've not given ourselves a proper opportunity to get results because we've given sloppy goals away and gone behind," Miller said.
"But it is more about when we concede. Take the St Mirren game, which we lost 2-1 - when the second went in, there wasn't a great reaction, which a team fighting for their lives should show. It was a case of 'here we go again, another kick in the teeth'."
Miller has found himself out of the side since January, starting just three of the last 12 games.
And, although, he has appeared from the bench in other nine matches, he has failed to score since the defeat by Kilmarnock in mid-December.
"It's been frustrating," said the former Scotland striker. "But I've got to sort my own game out and make sure I'm contributing in the ways the manager needs me to.
"The manager signed players in January and is picking the team he thinks is the one that will get results, so I have to respect that and play the role you I'm asked to play and, when called upon, make sure I'm effecting the game in a positive way."