Avalanche goalie Semyon Varlamov had 33 saves, including 16 in the third period.
"Give us credit, we stuck with it. I felt we should have had a point," Trotz said. "The scoring chances were pretty lopsided in the third period; they were about 15-1."
Palushaj and Tyson Barrie scored in the first period to give Colorado a 2-0 lead before Kostitsyn scored a power-play goal to make it 2-1 heading into the second.
The Predators (7-4-5) played most of the game without center Paul Gaustad. He left the game after playing two shifts with an upper body injury.
Notes: Barrie's goal was the first by an Avalanche defenseman this season. ... Duchene has scored a goal in four straight games. ... Wilson has a point in four straight games. ... The power-play goal Colorado allowed in the first period was just the second in 29 chances at home. The Avalanche killed off the first 20 penalties at home before Anaheim scored one. ... Nashville forward Patric Hornqvist was activated from the injured list and played his first game since sustaining a knee sprain Jan. 26. He missed 10 games. ... Avalanche defenseman Erik Johnson missed his third straight game with a head injury in the third period of a loss to the Phoenix Coyotes on Feb. 11. He is out indefinitely. ... Defenseman Shane O'Brien was scratched. Stefan Elliott, recalled from Lake Erie of the AHL on Sunday, was in the lineup.