Paul Hartley stressed his Dundee players are "desperate" to secure a top-six finish in their first season back in the top flight.
Wednesday's 3-1 win against city rivals Dundee United - their first in 10 years - put them sixth in the Premiership.
"Everybody thought we'd be struggling at the bottom but I've got great belief in my group of players," Hartley told BBC Radio Scotland.
"It's important for the players as they're desperate to get in there."
The Dark Blues trail United by two points and have two games to play before the league splits into top six and bottom six for an additional five matches.
Next up for Dundee is a trip to St Johnstone on Saturday.
"We'll take a big travelling support - probably 3,000 plus - to Perth, so I'm sure they'll be rubbing their hands," added Hartley.
"We were terrific tonight and the game-plan worked very well. We changed the team and went with a 4-4-2 diamond then adjusted and it was a great team performance.
"We've got a great blend of youth and experience."
Greg Stewart benefitted from Dundee United goalkeeper Radoslaw Cierzniak's howler to put Dundee ahead before Nadir Ciftci levelled from the penalty spot almost immediately.
However, Stewart went on to set up goals from James McPake and Paul Heffernan at Dens Park as the hosts registered their first city derby victory since November 2014.
"We're quite good at that - taking the lead and then conceding - we did it on Saturday," said Hartley.
"But they showed great character and good football. It's a big three points for us. James McPake had an outstanding game tonight; him and Stewart get the goals and great for Heffernan - he was different class."
Dundee United manager Jackie McNamara has now watched his side fail to win in 10 games.
"Extremely disappointed," he said.
"I thought first half we were causing them problems but the second half we didn't do enough to challenge them going forward.
"They're not bad players, they're suffering a little bit in confidence with the things that have happened in the last number of weeks so we need to put that right."