Killie could have effectively secured their berth against St Mirren at Rugby Park on Wednesday but were held to a 1-1 draw, and now must beat Dundee at home to guarantee staying in the top half when the league splits on Saturday evening.
However, Hay believes the demands of Saturday's game are incomparable to the tension they came through on the final day of the 2009/10 season, when they got the point they needed against Falkirk to stay up.
The left-sided player said: "There is a lot at stake but the club survived a relegation battle a few years ago.
"There's pressure but there is no real pressure. We will just go out and do our best and that's all we can do.
"With regards to the young boys feeling the pressure, they don't to be honest. They are young and confident and level-headed. They will just concentrate on their game, I'm sure of that.
"Obviously the likes of James Fowler and myself and even big Manuel (Pascali) - who is not going to be playing but will be in the dressing room - I think our experience will help. And you have guys like Paul Heffernan and Kris Boyd who have been over the course before.
"We will go out and give it our utmost best and hopefully that will be enough."