Leeds have slipped into the bottom three on goal difference with just three games left and now face back-to-back home games against two sides in the top half in third-placed Chelsea and ninth positioned Brighton.
The Whites will then visit Brentford on the final day of the season and Cooper says his side are confident of taking enough points to keep Leeds up.
Burnley - who have a far superior goal difference to Leeds - face back-to-back away games against Tottenham Hotspur and Aston Villa followed by a home clash against Newcastle United on the final day.
"As I've said many times before, this team does not give up," said Cooper, writing in his programme notes.
"We, as players, believe we can deliver what we need to in these final three games to ensure we remain a Premier League side next year.
"Tonight is our first opportunity against Chelsea and we know with the fans behind us, under the floodlights, that we can take a positive result from the game."
Cooper also provided a fitness update in his quest to overcome a recent knee problem that has forced him out of the last two games.
The captain said: "I was really disappointed to have to pull out of the Manchester City game in the warm-up, and then also miss the following game against Arsenal with injury.
"At this stage of the season, the last place I want to be is on the sidelines.
"I want to be out on the pitch helping the team.
"At the time of writing, I'm doing everything I possibly can to ensure I am able to feature in the final three games of the season."