Heffernan replaced Cillian Sheridan after his fellow Irishman pulled up with a hamstring problem moments before the break and proved the difference in a 2-0 victory at Rugby Park to keep hopes alive of a follow up to last year's Scottish Communities League Cup final win over Celtic.
"Obviously with the success we had last year in the cup, it would be great to get to Hampden again," he said. "That's what we want to do, we are taking this cup very seriously."
"That was one of the highlights of my career, getting to the cup final and beating Celtic at Hampden.
"In a cup on a one-off day anyone can beat anyone in the SPL so everyone is in with a chance."
The 31-year-old fired home in the 58th minute after Inverness debutant Charlie Taylor's clearing tackle ricocheted off the unfortunate Gary Warren and into Heffernan's path against Inverness. And, with the visitors stretched, he flicked home Ross Barbour's strike with five minutes left to put Killie in the quarter-finals.
Inverness also lost captain Richie Foran and playmaker Andrew Shinnie to injury in the first half hour.
Foran suffered a knee injury when Warren and a Kilmarnock defender landed on him following an aerial challenge, and Shinnie pulled up with a hamstring strain.
Inverness manager Terry Butcher said: "They could be out for a few weeks. It's just our luck, and the transfer window is closed.
"I must have made about five formations. Nick Ross played about four positions and Aaron Doran played about three. I don't think we had any luck. The first goal we concede, you can bemoan luck, but it's just not going our way."