The Hornets go into the weekend just one point adrift of second-placed Hull, who occupy the final automatic promotion spot, but boasting a far superior goal difference.
A draw against Leeds at Vicarage Road would be enough to seal Barclays Premier League football next season should Hull lose at home to champions Cardiff.
But Deeney, who has 19 goals to his name this season, is only focused on securing victory for Watford - a result which would force the Tigers to claim three points of their own.
"It's a very enjoyable environment to be fair," he told the club's official website. "Nobody's nervous or tense or anything. Everyone's quite relaxed about the situation.
"Obviously it's still not in our hands but all we can do is win our game, and hopefully Cardiff do a job for us."
Deeney added: "You don't want to be hoping that Cardiff win and we draw, we want to go and take care of it.
"To be fair, the way we've played all season is always to go and win games, so I don't think we'll start looking for draws now. We'll go there and hopefully we'll win the game and Cardiff will do a job for us."