Jimmy Calderwood saved two clubs from relegation and says Neil McCann must raise the spirits of the Dundee players.
McCann was appointed as Paul Hartley's successor last week, with the team sitting second bottom of the Scottish Premiership.
Calderwood guided Kilmarnock and Ross County to safety and believes man management is key.
"You've got to try to take the pressure off the players," Calderwood, 62, said.
Kilmarnock were the first to appoint Calderwood as a troubleshooter, bringing the former Aberdeen and Dunfermline manager in to succeed Jim Jefferies in January 2010, with the team second bottom of the top flight with 20 league games remaining.
Despite succeeding at Rugby Park, Calderwood was not appointed full-time and in February 2011 Ross County took him to Dingwall with the team second bottom of the second tier, then known as the First Division. Calderwood steered County to eighth place and safety.
Former Dundee, Hearts, Rangers and Scotland winger McCann has five games to try to move the Dens Park side out of the relegation play-off position, after a run of seven straight defeats resulted in Hartley's sacking.
"There's a certain pressure, obviously, and a lot of money involved," Calderwood said.
"It's very difficult, but the main thing is to try to keep them bubbly, lots of talking. It's no use them going in [with the attitude] 'aw no, here we go again'.
'You need to keep them with a smile on their face'
"There might have been times when you thought, 'I'm going to give him a rollicking', but that wouldn't work out. You would go up instead and say, 'is everything alright with you?' You would do a lot more talking than you would normally do.
"You try to keep them with a smile on their face, coming into training, making wee jokes - [assistant manager] Jimmy Nicholl was brilliant at it, so they weren't coming in with their heads down."
There have been other instances of Scottish clubs making appointments towards the end of the season to achieve safety, although not as late in the campaign as Dundee.
Kilmarnock brought Lee Clark to Rugby Park last season with the team third bottom of the Premiership table.
Clark's side finished in the relegation play-off place, but he oversaw a 4-1 aggregate victory against Falkirk across two legs to achieve safety.
The Englishman went seven games before winning his first match as Rugby Park manager, though, and Calderwood won only one of his first five games in charge of Killie. At Ross County, he drew his opening three games and won only one of his first seven, which illustrates that the appointment of a new manager does not always bring an immediate upturn in results.
This season, four Premiership clubs have changed manager during the season, with mixed results across their first five games.
|First five games in charge||Won||Drawn||Lost||Points|
|Ian Cathro (Hearts)||1||1||3||4|
|Lee McCulloch (Kilmarnock)||2||1||2||7|
|Stephen Robinson (Motherwell)||1||2||2||5|
|Pedro Caixinha (Rangers)||3||2||0||11|
Calderwood believes there is enough talent in the Dundee squad to steer the team to safety, with the bottom six sides now all facing each other in the remaining five games.
"It's not down to managers, it's down to the players," Calderwood said. "If you've got good people, okay you can have had a bad season, but you can still make it. You've just got to be as positive as you can be.
"If the players can take that on board, you hope they're going to be good enough and you can have the luck in the games."