Adams was a proud manager afterwards and admitted the victory was his greatest achievement in the game.
"Just a wee bit - 2-0 against Celtic, at Hampden, in the semi-finals of the Cup," he told Sky Sports.
"The performance was outstanding. We created chances, we kept retention of the ball and it's a magnificent day for our football club.
"The pressure was unbelievable. We had 7,000 people here today and to play a team of the stature of Celtic and to play so well, it's special. That's credit to all the players in the dressing room."
Adams claims his side always felt they were capable of toppling the Glasgow giants, with County able to boast considerable talent within their ranks.
"There weren't any nerves, just good players. That's what we do have in our squad," he said.
"There are no miracles because we performed to the height of our ability. It was the performance which won the game today and that's the key to performing at the highest level.
"Our game plan was to win the game today. At half-time we went in at 0-0 and I said to them, 'believe'.
"We came through the tunnel at Hampden, fans everywhere, I said 'do you want to do this again, yes you do'. That's what we will do come a couple of weeks time in the final."
He added: "Without a doubt. In 90 minutes of football it's 11 against 11 and we have the desire.
"We have just taken out Glasgow Celtic here and that's a magnificent achievement."