Craig scored the first after 55 minutes and Martin Scott sealed their place in the final with the second in the 88th minute as Celtic's miserable season hit a new low.
"Words can't describe this, it's Roy of the Rovers stuff," Craig said on Sky Sports 1.
"I could feel cramp coming after about an hour. The atmosphere and adrenaline got me through it."
Scott, a lifelong Hoops fan, simply could not find the words to sum up his joy.
"Absolutely delighted," he said. "It's not just individuals, the team was brilliant, soaked up the pressure.
"We are a good young team.
"A lot of boys in the squad have good ability, we had no fear coming here today."
Asked if the win was the greatest achievement of his career, County manager Derek Adams told Sky Sports 1: "Just a bit.
"The performance was outstanding. It's a magnificent day for our football club.
"This is unbelievable, to play a team of the stature of Celtic and to play so well is special."
He added: "Without a doubt (we can win the trophy). Ninety minutes of football, 11 against 11, we have the desire."